UGH.

As some of you might remember, I've just started running a lot this week. I have been really careful about stretching, toning, yoga-ing, etc... yet I still managed to sprain my ankle when least expecting it: walking to class. I slipped on ice and that was that.

So: I need to rehab this ankle ASAP so I can run in 10 weeks, but I also want to stay on plan and get some kind of cardio every day. What can I do (besides swimming -- no pool) and how should I protect my ankle when doing it?

You need to rest it or you'll damage it further. You could do seated boxing moves. Or just stick to sit ups, weights for a week or so. Then get a brace for it. Ankles can take a long time to fully heal.

For sure, I'm not running for the next 11 days at least. I'm just trying to figure out what I can do while toting it around, ideally still with my legs?

Why dont you just take a week off and let it heal? If you do ANY load bearing exercise its going to not heal properly/for a long time. Trust me, i ran my first 10 miler 2 or 3 days after seriously spraining my ankle (torn ligament) its never fully healed, and ive injured it twice since then.
as long as you keep your diet in check you can/will still lose weight even if you dont xercise for a week. Fat loss is about diet... you may even find that you lose a LOT of weight if you take time off from exercising, depending on how much you usually do ( i lose fatwhen i DONT exercis, personally)