How do I know if my router supports IPv6?

$ ping6 ::
PING ::(::) 56 data bytes
64 bytes from ::1: icmp_seq=1 ttl=64 time=0.046 ms
64 bytes from ::1: icmp_seq=2 ttl=64 time=0.053 ms
64 bytes from ::1: icmp_seq=3 ttl=64 time=0.058 ms
^C
--- :: ping statistics ---
3 packets transmitted, 3 received, 0% packet loss, time 1998ms
rtt min/avg/max/mdev = 0.046/0.052/0.058/0.007 ms

Is this evidence enough to know that my router would support IPv6? How can I tell without looking up router make, model and firmware on possibly outdated tables?

You can ping the "all routers link-local address" (RFC 4291) to discover all routers on your local network (replace en1 with the name of your connection interface, e.g. 'eth0' or 'wlan0'):

$ ping6 -I en1 ff02::2
PING6(56=40+8+8 bytes) fe80::def0:9abc:5678:1234%en1 --> ff02::2
16 bytes from fe80::1234:5678:9abc:def0%en1, icmp_seq=0 hlim=64 time=33.759 ms
^C
--- ff02::2 ping6 statistics ---
1 packets transmitted, 1 packets received, 0.0% packet loss
round-trip min/avg/max/std-dev = 33.759/33.759/33.759/0.000 ms

Have a look on http://test-ipv6.com/, I find it very helpful and quick.