If you have License for Second vCenter, you can go for separate vCenter for QA without any issues.
if you go for Single vCenter, You can make new Cluster for QA Host and Vms, still manage Networking, users VM permission separately. This is ideal for small setup.
Separate vCenter's are recommended for big ESX/VM Inventories and if you are using vCenter's for different purpose ( QA and prod still includes in this)
e.g. in My setup, We have separate vCenter for Development and IT Production servers, vRealize Automation...etc.
But again each vCenter's Host count is 80+ and VM count is 1K to 4K in each vCenter.
2) Domain question came in mind for below reason -
if you go for separate QA vCenter, There is no reason to do anything with prod Host and VMs.
You can use same network VLAN for QA Host management IP or go for new VLANs for all QA Host, VMs to keep network traffic separate.