A MOSFET gate driver chip will solve this. They take standard 3 or 5V logic inputs.
It is clearly the wrong MOSFET for the job. The resistance is way to high when you can only switch it on with 3.3 V (not matter how fast you can do it - speed is another problem).
You should look for logic level MOSFETs. I would recommend the IRL540, but there are many other options. Here is a link to a page that explains why:
You can use a MOSFET driver, but it is much easier just to get the a logic level MOSFET.
The diode across the motor is vital.
Also note that drawing 3A using a circuit on a breadboard using thin dupont wires is a problem in itself. You will probably not be able to draw 3A through the wires without them heating up significantly. You should have thicker wires from the MOSFET to the pump. It is a good idea to have a small heatsink on the MOSFET.
ReverseEMF:
It's my understanding that all of that is correct
Thanks RE!
All of this is a lot to take in. My head is spinning.
There is a lot of talk of using a MOSFET driver. This is something I'm looking into and need to learn about.
So far I was thinking of using IR2301 as a driver and supplying it with 5v from a buck converter.
As to the thicker wires. I think I'll knock something up using perfboard so the MOSFET is not directly connected to the breadboard.
I'm really appreciating all this input I'm getting from everyone. It's giving me a lot to think about.
larsgregersen:
It is clearly the wrong MOSFET for the job. The resistance is way to high when you can only switch it on with 3.3 V (not matter how fast you can do it - speed is another problem).
I know this is splitting hairs, and I completely agree with your wrong MOSFET assessment, but the OP reported that he/she was able to control the pump by manually toggling voltage at the Gate, so that suggests that the MOSFET can, with even 3.3V at the Gate, supply proper current to the pump after everything settles. So, it seems to me that speed of switching is a primary issue, and the cause of this deficiency is the poor performance of this MOSFET at 0 to 3.3V levels at the Gate.
Same conclusion, different reason.
If I use the IR2301 driver do I even need the buck converter? Couldn't I just supply it with the 12v?
Ppl39:
I'm really appreciating all this input I'm getting from everyone. It's giving me a lot to think about.
Whatever you do the diode is mandatory.
I'm afraid the IR2301 requires a minimum logic supply of 5V. And if you were able to supply the 5V to the IR2301 the input high minimum could be as low as 2.9V.
If you could find a way to supply 5V, you might try this device Mosfet Driver
BTW Sorry my last post was redundant 
I didn't see Wawa's 3.3v statement.
Ppl39:
So far I was thinking of using IR2301 as a driver and supplying it with 5v from a buck converter.
No, that's a high-low driver, you need just a low-side driver and you need to give it at least 5V for that MOSFET
if the datasheet says its OK at 5V (*). I've used the MIC4422 before which will definitely do the job (its actually
overkill really), many many other driver chips exist. Note that a MOSFET driver chip needs decoupling just like
any other chip, and 1uF or more ceramic is good.
(*) Some mosfet drivers may require a higher supply. The STP36NF06L MOSFET can handle gate
voltages from 5 to 12V and operate properly.
MarkT:
No, that's a high-low driver, you need just a low-side driver and you need to give it at least 5V for that MOSFET
if the datasheet says its OK at 5V (*). I've used the MIC4422 before which will definitely do the job (its actually
overkill really), many many other driver chips exist. Note that a MOSFET driver chip needs decoupling just like
any other chip, and 1uF or more ceramic is good.(*) Some mosfet drivers may require a higher supply. The STP36NF06L MOSFET can handle gate
voltages from 5 to 12V and operate properly.
Nay, sir. A push-pull affair is exactly what the OP needs. To say the OP needs "just a low-side driver" is misleading. But, I get the impression this is a language issue. I'm wondering if what you really mean, is, the IR2301 is designed for very high voltages, like 600V. And, yes, the MIC4422 looks like a winner!
Its a language issue, a low-side driver drives a low-side switch, as in the OP's circuit. Every MOSFET driver
can source and sink large currents whether high-side or low-side.
JohnRob:
I'm afraid the IR2301 requires a minimum logic supply of 5V. And if you were able to supply the 5V to the IR2301 the input high minimum could be as low as 2.9V.If you could find a way to supply 5V, you might try this device Mosfet Driver
BTW Sorry my last post was redundant
I've been following Great Scott on his YouTube channel and have seen him using a TC4420 driver with NodeMCU.
When I wrote this post I really wasn't expecting such great response. It's made me realise that I've got a lot to learn to do something that I thought would be simple 
I didn't fallow all the comends but it looks that problem is not solved ?
I think I've been given a lot of solutions to my problem?!
It's just a matter now of trying and testing them.
I'm going to use a MOSFET driver as many have suggested.
There was sugestion to use light bulb (12V from car) and 3A fuse.
I looked at datashet you transistor is ok, even has diode inside.
Your post #0 sugest me that PWM is shorting gate of MOSFET thas why I suggested repleace 150 ohm by 2K, those transistors are using voltage not curent for control, ......
so try this.
Better
Reduce PWM amplitude by potentiometer, 10k shouldbe ok.
D5 to one end , second end to ground , viper to 2k resistor and second end 2k to gate., Rotate potentiometer to see when motor starts to rotate = soft starting.
Tel me the results.
Correction - start with light bulb to be safe unless you have 1 spare MOSFET
Connect osciloscope to gate and drain
VGS(th) Gate Threshold Voltage VDS = VGS ID = 250 µA 2 V
ted:
Correction - start with light bulb to be safe unless you have 1 spare MOSFET
Connect osciloscope to gate and drain
Unfortunately I don't own an oscilloscope, I do have a potentiometer though
Try without oscilloscope.
MarkT:
Its a language issue, a low-side driver drives a low-side switch, as in the OP's circuit. Every MOSFET driver
can source and sink large currents whether high-side or low-side.
Ahhh... now I see what you're saying. The IR2301 has both low-side and high-side drivers. As long as the OP uses the LO output, it should work.
ted:
...thas why I suggested repleace 150 ohm by 2K, those transistors are using voltage not curent for control, ......
Yes, but for high speed switching, there needs to be enough current drive to charge and discharge the Gate capacitance. But, that shouldn't be an issue in this case -- with the correct MOSFET choice. But a MOSFET driver will make this moot.
Ppl39:
If I use the IR2301 driver do I even need the buck converter? Couldn't I just supply it with the 12v?
That should work. The IR2301 is good for up to 20V -- but, check to be sure the MOSFET [that will be driven by the IR2301], is designed to handle 12V at it's Gate.