will a long journey kill my already whining rear diff?

reason i ask is i have just found out i may be driving to lemans (1000 mile round trip-ish) and my rear diff (i hope) is whining when you let off the throttle.

how much should i budget for

a) second hand diff?
b) refurbished diff?

also how much work/labour is involved in swapping it?

cheers muchly