Stop enabling him to be such a lazy arse.
Tell him plain and simple “ I was up all night with our child, you need to make kids their breakfast, do the school run and wash the breakfast pots. I’m tired, I’m going to sleep until 11am. Do not disturb me”
Then when you get up, tell him to help with the running of the house. Give him clear, specific instructions. “The bathroom needs cleaning, the kitchen floor needs washing. I’ll do one, you can do the other. Which would you rather do?”
Make it clear to him that if he doesn’t go out to work he can pull his weight at home.
If he thinks it’s ‘womens Works’ to prepare dinner or do some laundry, then stop doing any of the blue ticket jobs you’ve been doing. (We have blue ticket jobs, pink ticket jobs here. If my dh says “the grass needs cutting this weekend” I just reply “that’s a blue ticket job” )
Establish what each of you will do.
Either he goes out to work or he helps you and you can both have set jobs.
Otherwise why be with him? If you’re doing all the hard work on your own, you might as well be on your own and if you were on your own at least you’d get every other weekend off from being a mum.
If you don’t let him know how you feel, he will never guess, men seem ignorant of our feelings sometimes.
Talk to him today. Best of luck, I hope you can work things out.