Tired momma

NBFR: My 12 week old is soooo restless at night from the hrs 3 am until she wakes up at 6am. When she is restless majority of the time she looks like she is sleeping thru it cuz her eyes r closed as shes turning her head as far as it can go to the left, making some noises, and lifting her legs up. I have been dairy free for 2 1/2 weeks in hopes that it will help with my daughters gas pains. Any tips or suggestions that might decrease her restlessness so we can all sleep a little better? Side note: she feeds about 2-3 times throughout the night