[Frosteater]

I'd say this is certainly a hand you can raise in that spot, but as Nemesis mentioned, it is read dependent. Usually I'd raise here, too, but if you have someone left to act who can't fold a hand for his life, this type of hand can get expensive pretty fast. Also the BB is really short so you are unlikely to take the pot down preflop. Again, a read dependent point, if you figure your hand ahead of his range, you might as well try to take the shortstack out of the game.

As for the rest of the hand, I second shove turn and actually either just call the flop or raise a bit more. It looks like you were raising to your drawing odds, but on the other hand it was a weak raise of a weak bet and it probably doesn't add much of fold equity and I think it's usually better to take a small pot down than facing a difficult turn decision. I'd make the raise somewhere between $0.8 and $1.2 , this also makes a shove on the turn easier and I don't think there's more of a thread of 3bet-push compared to your smaller raise.