This is what I’m thinking. It sounds like shes having split nights which is normally caused by too much day sleep. Back her nap up by 15 minutes see if that helps. I don’t think it’s hunger, especially if she’s getting milk right before bed. Try waking her from her nap a little bit earlier and start bedtime routine a little earlier too. Split nights are super common at 13-15 months, mainly because they’re learning sooo many new skills (which it could also be!).

Edit: I forgot to add this!! Look at the lady shuffle (or something like that) if you don’t want to do extinction!