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.
Yes you should. Never leave dogs (even the sweetest ones) with kids/babies without supervision.
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.