How do I get AVX support in QEMU?

It seems like if a defined feature is not available, it will fail silently by default (source). Qemu can emulate some instruction sets not supported by the host CPU, but I'm not sure if AVX is among them (or not yet).

Ensure that all the libraries used by Qemu, and especially libvirt, are up to the right level. You could also try the qemu-kvm parameters of -cpu sandyBridge,+avx,enforce. See also if this thread is useful.

For AVX and other new instruction set extensions, Intel provides an emulator:
Intel Software Development Emulator.
You could maybe use it instead, for gaining experience with AVX.