LSN is low sleep needs. If your DD is only taking a few sips of milk when she wakes at 4am, I might suggest switching her right over to water. It will be hydrating but also not as delicious as milk, thus giving her even less reason to wake at 4.
At this age, most babies are able to manage between 3.5-4 hours, so you could probably safely aim to push her a little in the mornings. Normally while the adjusting is going on, parents find that things go a little sideways in terms of bed times ect. as they try and find a new equilibrium every week or so. However, it sounds like your DD is doing well with one nap so I'd suggest sticking with her current bed time and just gently extend her morning A time. Most parents have the nap after lunch but that's totally up to you. When at home my DS has lunch around 11:45/12 and has his nap between 12:30-2:30. At day care, I don't think they eat until noon and he often doesn't go to sleep until 1! (not my ideal but c'est la vie)