There is limited benefit in using two VLANs with only one physical network infrastructue as that still uses the bandwidth available on the cables and all you gain is a security segregation.
A dedicated network with it's own LAN switch and NICs in each server gives you the bandwidth gains as the traffic is on physically separate cabling (as well as giving the security segregation - which to be honest is usually of minor importance in most environments)
Of course if your backups don't adversely affect the production bandwidth (possibly due ot the time of day they run) then leave it all on one network and keep it simple (don't overcomplicate things if it works)
