Sorry to hear about your injury. It really depends on how you feel coming out of the boot, where you are today aerobically and what your Princess goals are.
First, why the boot? Generally today most docs will attempt to push patients away from immobilization of sprains/strains so that the joint does not ‘lock up’ and the muscle does not atrophy. Not being the doc I am not second guessing just wondering. Assuming you come out of the boot around Christmas you will have about two months to get into half marathon shape. I would imagine that you will have a good 2-3 weeks of just losing up the ankle and getting use to walking again. From there it is all up to you and where you aerobic fitness is at the time and how fast you can adapt to the building up.
One thing that should occur if it did not during your visit today is to see what aerobic activities you can do while in the boot. It may be worth a follow-up call to get some direction if you want to run Princess. Ideal aerobic work would include spinning classes, or sticking with recumbent cycles if you are not allowed to put weight across the foot. Pool running is a great workout; especially if you have access to a pool that is 4-5 foot deep. You can purchase floatation devices that will keep you head up and then go through the running motion for 30-50 minutes at a time. Finally the row machine offers a great workout while in a boot – there are several workarounds that would allow you to stay in the boot on the machine including only strapping in the good foot or strapping in the boot. Talk with the doc’s PA to get advice. By doing these activities you will maintain some form of your aerobic base while recovering. No gym membership? Now is a great time to join a gym, most are selling for little or nothing to get in. Saying all this, you still need to create a good portion of time to allow for recovery. The body will force a lot of energy to the injury and you need to rest as much as needed to assist.
Finally, it should take a couple weeks to get running again once out of the boot and more than likely 4-6 full weeks to feel like you were at the point where you were pre-injury.