Hm... I don't know if it's different in other English-speaking countries, but in the U.S. (at least, in my part of the U.S.) I never hear "on to" being used like that. Occasionally I will say or hear the phrase "move on to [noun]" or "go on to [noun]" in sentences like "Let's move on to today's lesson," or "I'll go ahead and go on to the next question," but that's about it. It's pretty rare, at least where I live.