this thread pwnz
But anyway, I'll ignore all the previous junk and just post on the topic.
I'm not sure how your first accident wasn't at fault, but if that's true, it doesn't go as a point on your rating level. If they ruled it as partially your fault and you just think it wasn't, that's a different story. In either case, two at-fault accidents could get you canceled, but it isn't 100%. If there was an injury in either, you're toast.
You should have hit the deer. I would much rather stayed on the road and tried avoiding a direct collision with it (the deer could NOT be the width of a traffic lane). For all you know, there could have been a person, tractor, water pipe, or worse in that field. Be thankful it turned out as well as it did. Not saying most people wouldn't panic and do the same thing... just giving you something to think about if you get in the same situation again.
If by some chance you do get lucky and State Farm does agree to not drop you... you have a few options. One would be dropping everything but liability. Your car doesn't change the liability premium, so that way you wouldn't need to worry about what you buy. Also, if you had a third claimed accident within three years of the first, you're not going to be insured by ANYONE... so collision is sort of pointless to carry now. Other option would be to get a cheap car. Civic, Protege, or Corolla. People are totally confused about what the rating group for the car is determined by. It's 80% repair costs... not engine size.