Is a compressor with a 1 gal. tank big enough?

When you consider plenty of reputable compressors don't have a tank, 1 gal should be fine. I use on with a 3L receiver & it's worked fine for me (mostly large 1/72).

I would be more concerned about the general quality & output of the unit.

I have a compressor with one gallon tank- one of those pancake jobs.  Not sure what the 1:48 has to do with the matter. Do you want to charge up tank and then turn compressor off?  It will not even handle a 1:72 scale airplane.  If you leave the compressor turned on, it will cycle when needed.  It will pump up to set point (generally well above pressures needed for airbrushing), turn off, then restart when pressure drops below lower set point. A normal airbrush will not use air faster than compressor generates it, so it will indeed cycle.  Size of model makes no difference.

For airbrush use I would add a second regulator so pressure stays more constant. On some of these cheaper compressors the main set point is not adjustable, and way too high for airbrushing.

These cheaper pancake one-gallon compressors are noisy. I wear big ear-covering headphones plugged into a radio while airbrushing.  I would say airbrush cycles about 1/3 time on, 2/3 off, but without the headphones or other earplugs, when compressor turns on there is a real startle factor that is unpleasant, so some form of ear protection is wise.

excdn11

Good old Canadian Tire has a sale on compressors this week and one of them has a 1 gal tank.  Is this too small for painting mostly 1/48 aircraft.   It is a crazy low price of $35 but not much of a deal if the compressor has to continually run.  (They also have another model with a 3 gal. tank unit for $80, but I would have to earn a 229 badge to get that one.)

With a 1-gallon tank, the compressor motor will kick-on with loud noise every couple minutes. It depends on the on-off setting of the compressor. Even if you can pump the 1-gallon tank to 150 psi, it will not last very long if you turn the motor off. And it is unlikely that a $35 compressor can pump to high pressure.

If you want to take it home to try, make sure that it is returnable.