I suggest you populate it on the VLAN, its easy enough to change it back if you feel you dont want it there, but thats the obvious thing that stands out to me as to why your VLAN clients have no internet access.
Also Alex point on the NAT, I just checked, you probably need an outbound NAT rule as well, configured on the WAN interface with the VLAN subnet 192.168.51.0, and set to translate the address, but I think by default this should be automatic. So it should be just a check to see if its there. If its not there, duplicate the existing one for the LAN, and substitute in the VLAN subnet.