Yes, that would be the best time to transfer the mare over, as that gives you the option to breed her as soon as she’s able to be bred, if you’d like.
It’s best to contact mare owners early, though, since a lot of people do plan breedings far in advance, and I know that I, for one, am less likely to agree to lease out a mare if I’ve already picked out a boyfriend for her and am mentally visualizing her adorable, sure-to-be-a-gazillionaire baby. 
But…but… So you’re saying that I can’t just close my eyes, spin around in your paddock and finally point to something and say, “I want that one. Let me have that one. Why can’t I have that one? I want it, I want it, I want it. Why won’t you give it to me?”
I want to be able to lease anything I pointed to–be it pretty, pretty mare, lawn-mowing gelding, fence post or that adorable chunk of mud by your left shoe. Are you saying that my dream is impossible? Can I at least have your left shoe as a keepsake.
Ok, forgive the silliness. Back to being productive.
You can have the mud as a keepsake. 
I need my left shoe to go with my left foot, though.
You must be off your rocker, to let me walk away with something so adorable. I think I’ll call him Mr. Fuzzlesworth. He’s just so precious. I think I shall name the next foal I have in his honor–filly or colt.
But it’s getting late. Come, Mr. Fuzzlesworth. It’s bedtime for you!