As a counterpoint to all the posts telling you to wait, sow wild oats etc... from personal experience, it's lovely to get married and do all your conceiving in your 20s. The average age of marriage for a woman in the UK is under 30 and first birth in the UK is just past 30th birthday now. On the timeframe OP and DP have mentioned, she will probably be 28-29 when they have their first if all goes well, which is hardly outrageously young in comparison.
There's no best time, really. Advantages and disadvantages whatever you do. Different strokes for different folks. You shouldn't take any more notice of someone telling you that sowing wild oats for years is an inherently good thing than you would of someone telling you it's best to settle down early.
What I'm trying to say, is that being married doesn't make much difference to your relationship, or indeed your life.
Well. Ish.
It doesn't have to make any difference to how you treat each other, or how happy you are. It does make rather a lot of legal difference, especially if like OP you're considering reducing working hours to be at home with DC. Being married can make a great deal of difference to your life there. The DP in this scenario doesn't seem to want to hear that, which is something that would concern me.
Anyway based on your update OP, I wouldn't want to delay TTC. You're young, and ordinarily would have oodles of time on your side, but if there's any suggestion of fertility issues that changes things. I assume that's what you meant when you said you'd be pushing it to have another after 30. However I would also still be making it very clear that I wasn't prepared to have a child outside marriage.
I must say it strikes me as rather ridiculous to be prepared to buy a property with someone and have children together, but not feeling ready for marriage. If you don't agree with marriage on principle, fair enough, and if you don't want commitment ever/at such a young age, ok. But if someone is willing to buy a home jointly and have kids in their mid 20s, as this DP is, that ship has sailed!