Yes, you can use it. Look at the product specification for the details.
One problem with 12V is if the total current which Arduino sink exceeds ~200-300mA, the on-board regulator gets hot.
It is better to use 9V or less for higher current.
I don't think that 12V 1800mA is a good choice, even though it is just about in spec. Go scrounging as almost any smaller AC to DC supply would be better, and most people have relatives or neighbours who'd just throw away old 4.7V Nokia phone chargers (actually 7V) and comparable. Find anything DC >20mA and in the range 7 to 10 Volts measured. If it does not have the right connector for you then snip off its original, check polarity with a mulimeter, and solder to arduino Vin/GND.
Keep your 12V in reserve, as that has a nice voltage to drive certain types of relays, run motors, light automotive sidelights, or do other stuff like that in a separate circuit next to your ardunio low power circuit with linked common ground.
If it has a barrel jack, then yes, it will work - your power supply is within the specified range. The voltage regulator on your Arduino will get a bit warm, but that should not be a problem.
In order to tell if 1800ma (1.8 amps) is enough, you will need to add up all of the stuff you will attach to the pins of your Arduino, and you haven't told us what those are. If it's LEDs, most sensors, or a servo, then no problem. You can look up the specs of your peripheral devices, or use a milliammeter.