Children, agreeing on having them, not having them, and how to raise them, is one of the fundamentals of a relationship...

The others being, agreeing on fidelity, values, religion, etc.

My point? Well its very hard for couples to have a happy and healthy relationship when they disagree on the fundamentals. Because more often than not, its the few places where compromise isn't always possible.

From what you've posted, doesn't seem that the issue is that she can't have any more kids, but that she flat out doesn't want any.
Those are 2 vastly differing things, and spells trouble in the future... Resentment fosters quite easily.

Nowww, I'm not saying a good longterm relationship is impossible between the 2 of you. Buuut its gonna take a lot of work, probably more than your average couple.

My first suggestion is to find out the real reason she doesn't want any more babies.

Maybe if she shares the why behind her decision, it will be easier for you to understand, and in future maybe even accept.

Secondly... if talking about this openly and honestly doesn't work, and between the 2 of you, you can't find a compromise ( like the surrogate option you mentioned) well then I believe you two should attend couples counselling to see if this relationship is worth persuing in the long run.