Yes, that's right, Kyle.
To be a purist you could say "Where do I have to put that" or "Where must I put that" seeing that it's "dois" rather than "devrais".
I think Chrispy is trying to translate mettre/poser as the phrasal verb "put on", whereas "put" on its own is fine.
If you wanted to keep it as a phrasal verb you could say:
What do I have to put that on?
Chrispy - is my attempted translation of this last sentence OK? --- Sur quoi dois-je le poser/mettre?