"What time do you get up in the morning?"
That’s not technically wrong in the narrow sense, but it presupposes a rather special situation. The reason being, if you front 明天 you put it in the focus of the question (the linguistic term is “topicalisation”). In this sentence, that has the effect that it sounds like you are creating a contrast between “in the morning” and another time. Maybe the addressee regularly gets up at widely different times of day due to shift work. Or maybe the situation is like this:
- 我星期四很晚下班，晚上12点才能去睡觉。 (I get off work very late on Thursdays, so I can only go to bed at 12pm.)
- 哦。那星期五早上你几点起床？ (I see. So at what time do you get up on Friday morning?)
Here Friday morning is contrasted with the point in time that was previously in the focus (Thursday evening 12pm).
But unless there is such a contrast, I would put 明天 behind the subject.
TL;DR: I think a case can be made that 早上你几点起床 should be accepted, but unless there is a very special context, I wouldn’t use that word order.
The English word "forenoon" existst even though it's not in common usage (and I don't get why, because it's a very useful concept). That would be the literal translation of 上午. 早上 means "(early) morning", and is, I understand, a somewhat more informal term. "Forenoon", "morning" and 上午 can all cover the entire period from around sunrise to noon while "early morning" and 早上 only covers the time from... well, from sunrise to 8-ish, maybe?
In my native Swedish, of which I speak with more certainty, "morgon" ("[early]" morning) would be from 5 a.m. to around 9-10 a.m. and "förmiddag" ("forenoon") would be from around 9-10 a.m. to 12 o'clock. "Förmiddag" could, similarly to 上午, also be used to mean the entire period from 5 a.m. to noon.