OK, well, you might have to readjust your job expectations there. I have friends who graduated summa from Ivies and have still not been able to find jobs in public policy, or in any substantial government or NGO work. There are just not a lot of jobs in those fields out there, and those that exist are horrifically competitive.
But to answer your first question, applying in December isn't tragic, especially if you have all of your essays, LORs and whatnot lined up. The key here is to do well on the LSAT. If you do poorly, or even not as well as you would have expected, you should wait a year. However, if you hit it out of the ballpark, go for it.
My suggestion would be to have all of your supplemental stuff done, in anticipation of applying this cycle. Study your ass off for the LSAT. If you get pleasantly surprised, then woo hoo! If not, then you can go from there.