At her age, a 4 hr feeding routine is the way to go. However, if she is waking at night to feed still, she is either waking from habit or is not getting enough to eat during the day. Is she having 4 feeds and a df? This would probably be best. Have you tried a 3.5 feeding routine?
If she is waking at 6 am, you could try doing pu/pd until 7 am in hopes of resetting her internal clock to an appropriate morning wake time. It will take consistency and many days of doing so, but it can work. Then, get her up at 7, have a feed, have A time of about 1.5 hrs total, start a nap winddown, then put her down for a nap. If she wakes after 40 mins, do pu/pd again for either 40 mins or until nap time should be over. So, you would have E 7, A until 8:30, nap until 10-10:30, feed 10:30-11.
Now, if you are unable to get her back to sleep when she wakes early from her nap, the next nap would be sooner after the next feed as she is behind in her sleep for the day. For example, if she wakes at 9:15, and her feed is at 10:30, she's already been awake for 1.25 hrs, and would probably be ready for her next nap around 11 (after you have time to feed her and change her diaper if necessary). Just make sure she doesn't feed to sleep as that would create another problem for you to solve later. Just keep trying to get her to sleep so that she can stay up a bit longer in the evening an hopefully get back on track with her sleep. You shouldn't feel like you have to go by the clock, instead go by your dd's cues. If she looks tired, put her to bed.
I don't advise, though that you push her to stay awake later in the evening if she is clearly tired. She will then become overtired and find it even harder to fall asleep. I think that if she can get some more day sleep with better naps, then she will slowly be able to stretch her evening to a slightly later bedtime. However, some babies are just naturally early risers and there's not much you can do to change it. I have, however, read success stories using wake to sleep in the morning and also just going in, resettling with a touch and some comforting words and going back out. You may have to try a few different things to find what works. But for now, as long as she's going to bed at 5:30, she's going to be ready to wake at 5:30/6 the next morning as that is plenty of sleep.