I have a 4900M with the same problem except I am running 15.2(1)E. The latest config guide I can find for the 15 train is 15.0 which does not list DNS as being supported for VRF. However, there are some commands that make it appear it is.
Entering these commands...
ip domain-lookup source-interface FastEthernet1
ip domain-name vrf mgmtVrf mydomain.com
ip name-server vrf mgmtVrf 188.8.131.52
It still does not work...
c4900M#ping vrf mgmtVrf 184.108.40.206
Type escape sequence to abort.
Sending 5, 100-byte ICMP Echos to 220.127.116.11, timeout is 2 seconds:
Success rate is 100 percent (5/5), round-trip min/avg/max = 8/11/12 ms
c4900M#ping vrf mgmtVrf google-public-dns-a.google.com
Translating "google-public-dns-a.google.com"...domain server (18.104.22.168)
% Unrecognized host or address, or protocol not running.
I can ping and TFTP from my Fa1 interface, so routing is good. Looks like DNS is not fully supported yet, or am I missing a command?