We are building a server but one of the new disks is dead on arrival. If we put the os and apps etc on the first disk, when we get the bad disk replaced can any one see any reason we shouldn't be able to create a Raid 1 Mirror at that point?
It's easy to make a RAID-1 volume after installation using Windows software RAID. Assuming you're using Windows there's no reason to delay installation on account of the RAID.
Linux software RAID is a little more tricky to migrate into after installation but it's still feasible. It's going to depend on your distribution as to the procedure.
If you're using some other OS besides those two please update your question.