With ONTAP 8.1, you add disks to grow the aggregate over 16TB and it will automatically convert in the background (no downtime) from 32 to 64 bit. Growing over 16TB is the only supported method. If you search this community you will see some posts of a diag mode in place method without adding disks but that is not supported (diag mode command).
You can also replicate from 32 to 64 with ONTAP 8.1 and have a quick downtime while you cutover to the new volume but if you are on 8.1 then the best solution is to add disks and convert the existing aggr for now downtime.
QSM creates a qtree on the target volume for you.. So you can mirror any source qtree (or non qtree data by specifying /vol/volname/- ... the dash meaning non-qtree data as the source) and the target is always a qtree. You specify the source /vol/volname/qtree or "-" and the target /vol/volname/qtree.. the target volume can have multiple qtree mirrors if you want.
But if VMware and the goal is non-disruptive 32 to 64 bit (and not ontap 8.1) then storage vmotion sounds like a much better fit.