If I were you, I would spend more time with her chatting/reading stories before she falls asleep.
My daughter is older than your daughter, she still asks me every night to read stories and be with her before she falls asleep. I can see how much she enjoys our time together and it is easier for her to fall asleep. It also helps bonding with her.
I actually recorded many stories with voice memo on her ipad. She will be asked to listen the recording when I am not available :~(