Op, there's a vast difference between not wanting children and not being able to have any. Many couples struggle to have children, but the intention is there iyswim.
And committing to have children doesn't mean that you have to undergo fertility testing to ensure you can deliver on that commitment. when we talk about wanting to have children it's the process we talk about, because there are actually no guarantees in life.
When I was with XH we ttc for six years for a second baby. We had some tests, and at the time XH was told that he had a low sperm count, enough so that his fertility was considered limited. We never followed this up but XH said at the time that I should just leave him to have babies with someone else. My response to that was why would I? I was with him, we'd already had one baby, and besides leaving wouldn't mean I would run straight into the arms of someone else able to give me babies. However if at the beginning of our relationship he'd said that he didn't want children I wouldn't have married him, because our life plans would have been too different to be compatible.
Your dp actually sounds very reasonable in his approach, even down to the point of not wanting to have children with someone who would have them just to keep him. Children change the dynamic of a relationship completely, and if you were having them just to keep your husband, then that could create a lot of resentment and possibly end up in the relationship breaking down anyway to the detriment of not only the two of you but also the children you had in order to maintain the relationship.
You need to decide what you want as well. And if that means that perhaps you don't know yet, then you need to be honest about that. But while you still don't know whether you want children it is unreasonable to expect him to marry you. Because if in five years time you decide you don't want children and he decides that is a deal breaker, then ending a marriage is far more painful and involves far more upheaval than just walking away from a cohabiting relationship.