In much the same way that a new version of RIP has been defined for use on IPv6 networks, a new version of OSPF is in the works as well. Referred to as either OSPF for IPv6 or OSPF version 3, this new version is fundamentally very similar to the IPv4 version of the protocol, but which a few changes. The most basic of these is the fact that the addressing portions of an LSA packet have been changed to use IPv6 addresses and prefixes, as you may well have guessed. Other major changes include OSPF running on a per-interface rather than a per-subnet basis, and the removal of all authentication functions from the protocol. The IPv6 authentication header now handles all authentication responsibilities instead.
OSPF version 3 is still only a proposed standard going through the RFC process. However, all signs point to it soon becoming the standard for running OSPF on IPv6 networks.