AD stuff will come across in a system state backup, but hyper-v will need to be exported (via the command line, no less - GUI isn't complete). File Services is also more of a manual move, especially file shares and permissions there. I find it best to use a 3rd party tool for this (I prefer SecureCopy
because it works and can be rented). DHCP can be backed up and restored easily, and DNS should be AD-integrated. Print services will come over with some script work (check out \Windows\System32\Printing_Admin_Scripts\ on your print server).
If you can, it is 100% better to have both machines up on the domain at the same time. Otherwise, this is more like a disaster recovery exercise than a replacement.... and I'd prefer never to have to migrate to a new server like that, ever.
Ultimately, though, you'd be better off virtualizing ALL of these roles on hyper-v (assuming not a cluster)..... then server migrations would be simple VHD exports from one box, imports to another, and potentially integration component upgrades if necessary once booted on the new box. Just sayin'