
It will cost a huge amount if you choose to fly the pup into UK and probably won't save the pup a huge amount of time in confinement as they only allow dogs into UK as Cargo.
This requires the pups to be deposited with the cargo people about 5 hours before the flight.
You then have the flight of a couple of hours, then it has to go into the animal reception for you to pick up, again some hours will elapse.
I would always choose to drive with the pup. This enables you to stop to see to it's comfort. I have had pups go to Scotland from here and that can be a 12 hour journey.
As to the passport a puppy must have a Rabies vaccination at 3 months of age at least, and can then travel to UK (or other EU country) after 21 days. You do have to use and approved entry point/route.