We both work full time, but he always moans about things around the house and says I don't do anything even though I do most of the washing, I hoover, I clean up after dinner.
So you both work full time, that’s equal.
Who genuinely does most of the housework do you think? Being honest? If you can’t work it out or don’t trust yourself to be able to assess, maybe write down together what you’ve both done in the last fortnight re housework.
Because just from a glance at the situation, doing the laundry, hoovering and the pots after dinner is only a small part of the overall picture of what it takes to keep a house running.
For example, who makes the beds and changes bedding? Cleans the bathroom? Mops the kitchen floor? Cleans the kitchen? Cleans the fridge out? Does the ironing? Puts clothes away? Dusts everywhere? Tidied the mess away? Takes the bins out?
If you do do 50/50 with him (until recently when you’ve been sick of course, which would mean either partner should pick up the slack whoever is ill), or to be fair if you realise that both of you do equal, I think the only way forward is a boring housework rota, which will either even out the chores and make him feel it’s more balanced, or prove to him you do pull your weight.
Write down everything that has to be done daily, weekly and monthly (there are lists online if you need a guide) and decide on a rota for who does what when.
i can see your perspective feeling you already do enough, but I know from my own relationship I do lots of things OH claims not to see or notice or that don’t bother him, so even though he’d say it’s pretty even I’d disagree and over time the frustration can grow, and it’s a tense time for you both now as you’re newly cohabiting and if he’s feeling like you’re coasting re the house he might be scared now that you’re stuck together with a baby, just like you’re scared in case he is a knob and you’re stuck with him in one way or another.
So I wouldn’t be so quick to jump to LTB, not with a baby on the way and without seeing how you can work together to resolve this. Nobody can argue with a black and white rota you’ve both agreed to and adhered to. Do you think he’d be up for that? If you suggest it it’ll show willing if he’s convinced you’re not doing much around the house.