MosFets are voltage controlled devices. The gate draws essentially no current. The voltage you put on the gate creates a field in the device (hence the name).
Specific to your application:
Look in the datasheet for a specification called Vgs (threshold). In the Fairchild datasheet it is on page 2. It is the top line of "On Characteristics".
It is specified as somewhere between 2 and 4 volts. This means the FET will START to turn on (or turn on slightly) somewhere in that range.
Now look at Figure 2. It is telling you to get a few amps of FET current the voltage at the gate must be above 5V or so.
The long and short of it is that (as the others have said) you must find a MosFet with a Vgs below the 3.1 - 3.2 volts you will be putting on the gate.
It is a good idea to put a couple of kilo ohms in series with the gate so if the MosFet fails it will not take your processor with it.