Early wake ups and lack of day sleep

Hi! My little girl is 9 months old and has just started nursery. Since starting she doesn’t seem to be sleeping through the day very well and is waking up every morning between 5-5:30am. Prior to starting nursery we did a lot of contact naps but I did start to put her down in her cot for naps in the day so she could get used to being put down when at nursery and it was going really well. However, now I am lucky if I get 30 minutes out of her before she wakes up crying and wants to be rocked back to sleep and when trying to put her down her eyes spring open. I am aiming for 3-3.5 hour wake windows and will normally put her to bed in line with these but times often vary due to often being difficult to get off for a nap in the day. Nursery are saying she doesn’t sleep a lot there, maybe 1-1:30 all day at best in a total of 9 hours. Any ideas how I can encourage her to stay asleep when I put her down in the cot. And what I can do about the 5am wakes up because I am exhausted! Thanks