That thin, if you're having problems it likely isn't a gas flow issue. If when you pull the trigger, you hear gas flowing at the nozzle, that's usually good enough. I usually only run about 5-10 lbs of pressure. I usually never mess with gas pressure, just adjust wire speed and heat.
On really thin, what Rzucker says about just tip tapping across it works pretty well. Have the heat cranked way down, and that should "automatically" slow down the wire, if its a unit without separate wire speed adjustment.
I prefer a machine with separate wire and heat control, but what you've got is what you have to work with.
If you are just learning mig, practice with some 3/16 or 1/8" thick for a little while, then go down to the thinner metal.