As a physics bsc student, I have a very limited knowledge of QM:
Dirac formalism, Schrodinger equation and simple solutions (oscillators, particle in a given potential, hydrogen-like atom etc). There are more advanced QM courses I can take, but I find more interest in QFT.
What are the prerequisite subjects of non-QFT QM courses I should learn before starting with QFT?
You definitely need a good amount of advanced QM, but you don't necessarily need it all in order. What I did was just dive in and fill in the gaps (I was reading QFT books before I officially took QM). This approach may not work for some, but it's worth a try. Have a look at 't Hooft's subject list to get oriented. Also have a look at page 8 of Srednicki's QFT book (note the preprint version is available for free download) and maybe dive in to the first chapter or two and see where you get lost!
You will mainly need to see angular momentum (especially the algebraic approach and spin-1/2), time dependent perturbation theory and scattering theory, with enough complex analysis to handle contour integrals and residues. It would help to know the Heisenberg and interaction pictures, but a field theory text probably reviews those anyway. If you get exposure to path integrals that is fabulous.
You could also try the free chapters here.
Relativistic quantum mechanics is relevant for QFT. Often, a short introduction to relativistic quantum mechanics is given at the beginning of QFT courses if it's not a requirement.
Many-body quantum physics often introduces QFT itself through a different angle (namely that of 2nd quantization) than pure QFT courses which typically adapt a particle physicists' point of view. I don't actually know which order its preferable here.
