I just responded in OP's other thread, but I'll copy it here too:
YES. Given what you describe, she probably is pregnant, although it would have been better for her to grow up a bit more first.
I suggest you separate the two of them for at least 35 days (that would be sometime in the middle of January.) Adjacent pens, with wire mesh between them so they can still sniff and socialize, would probably be best. The idea is to prevent mating, but not separate them far enough to be lonely. And no playtime together-- none at all, if you want to prevent mating.
Definitely make sure she has a safe place to give birth: maybe a wood nestbox and lots of hay or straw to burrow in. The box can also be metal, plastic, or probably even cardboard, but the doe definitely needs plenty of hay or straw to make her nest. The opening should be high enough that jumps up and in, rather than walking in straight. That helps keep the bunnies IN the box while they are little-- so a top opening, or one partway up on one side.
A rabbit pregnancy usually lasts 31 days, so within about 35 days from separating them you should know for sure. Having the male separate ensures that he will not breed the doe (if she is not pregnant yet), does not trample babies when they are born, and does not rebreed the doe after she gives birth. Yes, a male rabbit can rebreed the doe before you even know the babies have been born, if he is in the same pen with her.
Then, if she has not yet had a litter, think about whether you ever want them to breed. If yes, make your plans and act accordingly.
If you know already that you do not want them to breed, you can have the male neutered now, and the doe spayed after she raises the litter, or if you discover that she wasn't pregnant you can have her spayed after enough time passes that you are sure of that.