I have 2 loving dogs that would not hurt a fly but I still wouldn't trust them. I would never leave them alone just never now.
Yes you should. Never leave dogs (even the sweetest ones) with kids/babies without supervision.
No I would not worry because the dog is a pit bull. Every dog is different. The other poster is right though that you should never ever leave even a trusted dog alone with a baby. Babies are strange to dogs and they move differently, which can startle dogs. I have a Great Dane and a little girl who is turning 3 in May. He has always been wonderful with her but they have never ever been left alone. I just won't take the chance with my daughter and I refuse to put my dog in that position. It takes extra diligence that's for sure but can be accomplished without issues.