Please be aware that you have no financial security if you split up and are not married.
I'm not saying you will split up of course, but you could potentially end up being a single parent of two children with no financial support.
You said in your OP that your partner thinks you don't have enough time for one another at the moment - and you think you can go back to that post-babies.
You can't. It gets harder when you have more children. It doesn't mean that your relationship becomes easier once your children are no longer babies - you wait till your baby becomes a toddler - and then you're thinking of adding another baby to the mix?
That's fine and most of us have done that. But to think you'll have more time to work on your relationship once your children are out of babyhood is very short-sighted.
Having said all that, if your partner is prepared to look after you and your first baby while you're pregnant again and on bed rest (and the baby will be a toddler by then, so much harder to look after) and you're willing to take the risk of having DC with a man to whom you are not married, then crack on.
Personally I think you are not really seeing what is absolutely going to happen when your baby starts to walk, talk and have tantrums.