Hi, this is my first post, hope im doing this right? 
So my DD is 6 weeks old tomorrow, she was also born 6 weeks and 1 day premature meaning her due date is in 2 days. She was born at 4lbs 7oz and was in NICU. Now, i work in a nursery setting, i understand children grow at their own rate and every child is different, but im starting to question my LO. Ive never had a newborn and not many people I know have had premmies, so i don't have anyone to ask?
Around 4 days IN NICU
she began lifting her head back with alot of strength when wed be doing kangaroo care. She also would occassionally use her arms to push back off me and quickly mastered that.
At 4 weeks 2/3 days she began to use her legs to get herself where she wants. She would use them to push herself up my body during tummy time. It began as a reflex but now at 5 weeks 6 days she almost uses them everytime we cuddle to push herself up my chest, same with dad.
At 5 weeks 2 days she learnt how to roll over, she tucks her knees in and uses her arms to roll onto her front. Shes never gone from front to back but i think its because she likes it on her front? 
At 5 weeks 5 days (yesterday) she started to push up on her arms to look around, moving her head from side to side and can do this for about 5-10 seconds before flopping on my hand (which is placed worringly between her head and the surface).
Yesterday was also the first time her gaze followed my eyes/head, i kept moving side to side and she concentrated for about 30 seconds looking at my face. Her eyes followed me left to right and right to left.
Lastly, yesterday night she had a hyperactive burst for 3 hours straight, she was lay on my chest and "playing" with her lips against me, coo-ing and flaring her arms and legs.
She wasn't hungry as she had a feed and rejects it when shes finished, i kept offering thinking that could be why but no? It was amazing to watch my little 6lbs 3oz baby using her arms to push herself up and look around, at me or reach to nuzzle my face.
Am I overreacting or should she -not- be able to do these things yet, where is the muscle mass? What is going on, is this all normal?
I guess I just want some advice on others babies and if this is normal as im waiting to see the health visitor and dond want to sound like an idiot. 
Also, DD has been combi-fed by bottle from birth and is a big eater, roughly 200ml extra a day.