prefernot, what happened this morning?
i've been puzzling over this. if you think that she wakes regardless of milk, why not hold it back until breakfast time? ie, even if she's not having much, by giving her it you're still giving her permission to start the day earlier than you'd like it to, whether she goes back to sleep or not afterwards. it's a bit of a signal, no?
from what you've said, you've got lots of factors in your favour ie, you don't believe she's waking for milk, and you do seem reasonably confident that she needs sleep than she has been getting recently, because of going back to sleep/needing to nap earlier so it does sound to me like she's just got into a pattern. well, it doesn't have to be permanent.
i think you have to decide what is acceptable, let her know, and stick to it.
but if you don't believe in your heart that she will be able to go back to sleep, then i guess that's an end to it -- your day is going to start earlier from now on.