Hi MSC,
I'm sorry that the axe has fallen for you!
We don't advise waiting until the very last minute to make your phone calls, to give time to allow for problems. Other than that it doesn't really matter when you initiate the claim.
The phone call will start the clock on the claim, I would expect the PIP2 form to arrive in around 10-14 days.
The things you will be asked during the phone call are explained in the PIP guide
PIP help for claimants You will be allowed 1 month from the
date on the form to get it completed and returned. This includes postage each way, so it is more like 3 weeks in effect.
DWP usually give an extra 2 weeks on request. Phone them and ask when the form has arrived.
Please reply to this with further questions or comments and we will do our best to help