IFR
In theory its 30mins within your countrys FIR and 1 hour if its an international flight.
In practise if its submitted directly to Eurocontrol electronically it can be a matter of seconds.
I think the reg is one of the few things you can't put a change message through about. Sneaky suspicion you have to cancel and refile if you change the reg. Which is one of the reasons why most commercial flights use call signs so you can swap airframes about without having to muck about with the flight plans.