Does qpopper supports IPv6?

In short: no.
In long: you can patch the latest [ftp://ftp.qualcomm.com/eudora/servers/unix/popper/ qpopper] with patch available [http://www.imasy.or.jp/~ume/ipv6/qpopper4.0.9-ipv6-20060626.diff.gz here] to support IPv6. In FreeBSD if you enable IPv6 with WITH_IPV6 options globbally in /etc/make.conf, then all your packages compiled from ports comes with IPv6 support, including qpopper.