Great, I have the same goal for my compiler. I'd love for the compiler to be able to bootstrap its own backend, and as it only compiles C that would rule out llvm.
I am not sure how far I am along in actually compiling C, if I'd had to guess I'd say around 60%. Hopefully there's not too much crazy things on the horizon.
I'm not a C programmer myself so I first implemented the switch statement in a naieve way, and then I discovered the way they actually work and spent days getting it right.
If I get to the point where I can compile trivial C programs like the benchmarks game, I'll research a move to QBE :)