"My mouth is watering" or "that makes my mouth water" is a neutral, polite thing to say (Oh, that smells so good, it makes my mouth water.") "Slobbering" has a much more negative, messy, impolite connotation - "Your dog is slobbering all over me!"
"A slobbering baby." calif jim is right, 'make sb's mouth water' a traditional idom and the idiomatic compound 'mouth-watering' are the only ones corresponding to what you intend to say,where as slobber has a rather pejorative connotation, and 'slobber over' has a totally different meaning( behaving in an excessively sentimental way towards someone). Be careful while using 'slobber over.'