7 week old struggling to sleep in the early hours

Hi!

Hoping to get some advice please surrounding my 7 week olds sleep pattern. 

She naps ok in the day from 30 mins to 4 hours on occasion, but usually needs the car or pram to get off to sleep. Then at night we manage to get her down by 8pm and she's in a deep sleep till 12/1pm which I'm so glad she's getting and feel that's really good at 7 weeks. I feed her then she'll go down for another 3 hours on average, but when we get to 4/5 am she's grunting, squerming, throwing her legs about and not sleeping well at all. she doesn't cry however doesn't sound settled and happy. She passes wind well at both ends generally throughout the day and trumps a lot during these hours / sleep stage. I try to soothe her in her Moses or feed her when to settle her through these hours, but I'm wondering if this is common and a phase? Will it pass and is something we just have to get through? 

She's not only keeping herself awake in the early hours, but my sleep is very broken as it can take up to an hour after feeds in the night to get her back to sleep. 

Any advice would be greatly welcome, thanks Sarah