Am I being unfair?

My boyfriend, when he works days has to be up at 3:30 in the morning. So I never bother him to do anything with the baby especially during the nights. But my daughter is going through a stage of going to bed around 2-3am and waking up at 5-6am she's not napping through the day and becoming increasingly cranky. I keep having break downs I'm exhausted, I'm drained and feel like I'm going insane. But I feel so bad because I have so much resentment  towards my bf when I just see him asleep getting all the rest he needs not even batting an eyelid to help out. I understand he has his job and this becomes "my job" but I'm struggling and I didn't create her alone. I'd prefer him to offer to help (which he never does) but I'm getting to a point where I'm gonna ask but am I being unreasonable? Btw even on days off or when he's home he sees it as me that has to do everything baby related and will happily sit on X box while I'm constantly up and down with the baby and if I ask him to watch her ( which I shouldn't have to ask him to babysit his own kid ) he'll make it very literal I'll come back out the shower for example and he's on his phone and she's in the exact same spot I'll ask him why he didn't play or interact with her and his excuse is always "because she didn't cry"