|MadSci Network: Chemistry|
Your initial thoughts just slightly led you astray. It is not the carbonyl oxygen, but the hydroxyl group which is protonated. This transforms it into a good LEAVING GROUP,(H2O)+. The amine attacks at the carbonyl carbon, as you correctly state, liberating a proton in the process. The water vaporizes out of the equilibrium, thus driving the reaction to completion.
Try the links in the MadSci Library for more information on Chemistry.