Our little 4am alarm clock!

Since around 5 weeks DD has been waking around the 4am mark for no reason. DH goes to work at 4am and at first we thought she was waking as she could hear him but she does it on weekends also. I have tried going in and giving her the dummy back but it doesn't work and she'll keep crying. I usually try the dummy 3 or 4 times before I give up and get her and bring her to bed with me. She will either sleep on me or take hubbies side of the bed as he has gone to work. Immediately she is back to sleep so judging by this I have assumed she is not hungry. She will go back to sleep till around 7am or even longer some mornings as I'll get up as she has been stiring and I'll make up her bottle, go the bathroom, make myself a cup of tea etc all while she stays asleep.

I've also tried feeding her at this time and she'll eat and go back to sleep. So ultimately I'm not sure if she is waking out of habit, cause she is cold (which I think has been the case as I've gone into her and her face is cold, or she has escaped her wrap, or kicked off her blankets) and she feels cold to touch so I warm her back up in our bed with lots of cuddles.

It also doesn't appear to matter what time she went to bed the night before. She can go to bed at 9pm, 11pm or after midnight and she still wakes at 4am. There has only been about 4 or 5 nights since she was 5 weeks where she has slept through to 7am although if i feed her after midnight it does seem to guarantee me a sleep in till 7am.

I'd love to get her to sleep 7 till 7 but no idea how to go about it or even if that is possible at this age yet. I've read the "Save our Sleep" book with the sleep routines but because these go by feeds etc and Chloe is demand fed it's really hard to get it to work.

If anyone has any suggestions I'd love to hear them in the interest of me getting some more sleep. Once she is in bed with me I wake alot with her moving and the cute noises she makes.