I need to deep clean my daughter's closet. The carpet is medium length plush carpet. It's not flat carpet but it's not the real high stuff either. I have a Bissell Proheat 2x that I bought back in May. It uses heated water. How long should I wait before putting her toys and stuff back in the closet?

It's not a matter of time at all.

Wait until the carpet is completely, fully dry, however long that takes. You can speed it up with increased air flow, like fans.