Having REP tokens on a Ledger hardware wallet, will I have to do when Augur protocol v2 launches?
In the V2 version of the contracts there will be an all new Genesis Universe with its own Reputation Token.
To use REP with the V2 contracts you'll need to own this new Token instead of the current V1 Reputation Token. V1 will continue to function as normal however.
REP holders can migrate their V1 REP to the V2 REP contract anytime they wish, which will destroy their V1 REP and grant them and equal amount of V2 REP.
There is no hurry to migrate from V1 to V2, however in the event a fork occurs in the V2 contracts it will be important to migrate and choose a child Universe before the fork ends. If REP is not migrated to a child universe in the V2 contracts it will not be able to migrate ever and thus be stuck in the old V1 contracts or the forked V2 Universe.
Edit - Addition from @achapman comment:
Migration will be entirely handled via a UI in the v2 compatible UI that is released along with the new contracts. It will be clicking a button and signing 2 transactions to migrate your REP.