Hi,
If she doesn't already has a sheltered place for the nest give her a nest box right now, noone can tell how far she really is, but with my does nestbuilding is a sign that they'll kindle soon.
Moving a pregnant doe is imho not a great idea, moving can cause stress since one of the most important things for rabbits is to know their surroundings. I would not put her somewhere she isn't used to be if there arn't very good reasons for it. If she's used to being in that place indoors and when it's really cold outside (well below freezing) I would consider it, but be sure that buck is not, in any way (my buck climbes 5ft obstackles and jumped down a 9ft wall to get to a doe) able to get close to the doe.
Give her lots of hay, a nestbox (A cardboard box as long as the stretched out doe and half of that width and about 10-12"hight with one hole just big enough for her is one option, there are other designs out there, I prefer closed wooden boxes) shield her hutch against wind.
Also, when you think it's getting close check regularly, when she starts plucking fur every hour, it can happen that kits are born or dragged outside the nest, and you'll have to act fast if this happens.
Read up about this, if you find a cold kit it is not necessarily dead, warm it up and return it to its silblings when it comes back to life.
Haystaching is a good sign that she's on the right track, but check the nest anyway, if there isn't enough fur to keep the kits warm you can pluck some more or supplement it with dryer fluff, or so.
Rabbits mature between 3 and 5 months, when your doe wasn't pregnant before 9 months that had other reasons.
Anyway, good luck