I ordered mine at the end of June and picked it up on November 10th. So not too bad.
Yes, I did buy the plate separately. I've been leasing my cars for more than 25 years, and could never be bothered with changing number plates. But this F-Pace is likely to be the last car I ever buy, so I looked for a suitable plate at the DVLA.
I tried to buy one in an auction, GSD 2J, but I was outbid. The one on the car was just available to buy now. I just searched around for something that would complement the car or my initials. Luckily I found one that does both.