As I am fond of saying, getting married will change your life, but having kids will REALLY change you and your life Forever.
If this is not something you ever wanted, pay attention to that; it's okay. As long as your H is good with that. Having a great life together is a worthy life too, ya know? Your path may be a different one.

Your body may be telling you something, but actually, you have lots of time to listen and decide.

My daughter is going through this right now. She is 10 years older than you so she is really thinking hard about what she wants the next 20 years to look like. In her case it's; a) slave to child or b) living happily w/her H & doing other worthwhile things.
I have assured her I will not be the mom begging for grandchildren, (but I wouldn't hate it if she presented me with one either.)
Money is a major consideration for them, they have it, but know it will take even more than they are planning to need for a future with kids.
I think your thought of caring for a living thing, like a dog, is a great idea. It will give you a taste of parenting.
And hey, you are still so young. You have lots of time....