if OP was posting here that she was desperate for a baby and her dp was stalling people would be urging her to consider the fact that he may never want children and to consider whether she wanted to stay in a relationship with him, in fact, people would be urging her to leave while she was still in charge of her fertility.
Now the dp is eager to have a baby and she isn't and still he's the one at fault and she should be the one to leave.....? 
Ultimately, both need to be on board with the idea of having a baby, but it's not uncommon for one party to be ready before another. Also, the op said that many of their friends have recently had babies, we don't know the circumstances, perhaps some of them struggled to conceive and op's dp is now concerned that if they struggle they may leave it too late
He's not wrong to be concerned that there could be issues conceiving. One in six couples have fertility problems so the statistics are very real, and while infertility doesn't discriminate in terms of age, the fact is that the older you are when you discover you have fertility problems, the less time there is to be able to deal with them if necessary.
That being said, nobody should have a baby they aren't ready for, so op isn't wrong for wanting to wait. but neither is her dp for wanting to have the conversation and to establish whether or not children are in the ultimate plan. Because if they're not part of op's future plan then her dp needs to start thinking about his own future and whether he wants to stay in a relationship with someone who potentially doesn't want to have children with him. Of course, if op does want children then she will tell her dp this and hopefully they will wait until they're both on board with the idea. But children is a fundamental discussion which should be had in any relationship.