You can still AA it, even if you plan to use it in a game. As long as you only AA pixels on the inside(the inside includes every pixel that doesn't directly have a pixel of the backdrop next to it) it should be no problem to put this on different backdrops.
Not sure if the red dots are both meant to be eyes or if the lower one should be a mouth. If it's a mouth, I think it would benefit from different colors than the eye or maybe a position and shape change would also bring it out more clearly as a mouth.
