yeah, it seems your suggesting the auto is at fault, a common mis conception with stalling cars it is not always the transmission/gear box.
In a manual it could be the gear box and is usually the drivers fault
Sounds to me like either your air intake is a little blocked, or your fuel line is a little blocked, could be a failing pump (As stated above) or a blocked fuel filter (As stated above) or a stuffed air filter prehaps ? maybe it needs a clean too.
Now having the air con on also makes it worse, this makes me think your belt could be old and well worn, or your battery is on the way out, could be the ignition system, since on idle it is ok, but when the spark plugs are put under load they could be failing.
allot of possibilities, easy sollutions first.
Clean Air filter, check fuel lines, maybe even replace fuel filter.
check your battery witha multimeter, could even be the alternator but not likely as after a few weeks and alternator problem will result in allot of other problems too.
Keep us posted on your progress.