Thanks for the replies. She is 16 weeks and was born 3.5 weeks early. Developmentally she is at about 16 weeks but her weight is still closer to her adjusted age.
She wakes at 6-6:30 most days and I do feed her and put her right back down because she always seemed too tired to be up for the day. She is now used to that and falls right back asleep until 7-7:30. At that point, she is wide awake, grinning, babbling, ready for the day. I get her up, feed her only if hungry (50/50 on this because of the 6am feed), get her dressed and play until she's tired. She is always eyes closed asleep an hour on the dot after she wakes up and awake again 30 min on the dot after that.
This morning I tried leaving her in bed and giving her the pacifier and a toy to see if she would wind herself down and finish her night sleep. She dozed off for about 5 minutes and was back awake again, so I got her up. She then fell asleep an hour later for 30 min as usual.
Night sleep is bad. We are working on it. She is going down at about 7. We have put her in bed as early as 6, depending on tired cues. She will fall asleep but then wakes up, needs settling, and falls back asleep for good at 7. She wakes every 2-3 hours all night long, occasionally sleeping through the first one. We can settle her with the pacifier during every other waking and but she won't settle without being fed on the others. She does self settle during her naps.