I’m so sorry to hear of your recent loss. I’m glad to hear you are looking for a new family member to fill that gaping hole.
So…
Most of what you need to know to get started importing a dog can be found here:
Typically a puppy can be imported from 56 days on.
(There is an exception where pups younger than 56 days can be imported provide the pup travels here and back with the mother… but I assume that would not be the case here.)
Dogs younger than 12 weeks can enter Switzerland without a rabies vac, however there is paperwork to be done. It’s an attestation that the pup has never, from birth, been in contact with an animal where rabies risk is present.
(As an aside, the cases I know where this was applied for were from an EU country with no rabies risk.)
If possible wait until the pup is fully vaccinated. It’s better for the pup, easier on you, and most reputable breeders will want you to do this anyway. You can reserve the pup (and visit if you wish), and then take him home definitively at the proper rabies vaxx age.
The BLV site has an interactive checklist to help you determine what you need to do when.
Key point: Make sure that animal control is open at the the border crossing you are going to go through! I cannot stress this enough. You need the border stamp - without it, a world of trouble and tears can await. Plan your trip accordingly, and call ahead to make sure that there will indeed be someone there to stamp you in. Not every border crossing is equipped for animal importation control.
If you plan everything and still find no one is on duty at animal control, find a hotel for the night.
If you are flying outside of Aminal Control hours, I think there is still an option to board the dog at the Zürich airport until the next day so you can do the import when Animal Control is open. Do check on that for updated info, however.
There have been times I’ve had to almost arm-wrestle the officer into taking the time to check my dogs in. They sometimes try to waive you on, especially if you are in rush hour traffic - but don’t let them. Seriously. Do not, under any circumstances, enter Switzerland with a dog that has not been correctly imported - even if it’s not your ‘fault’. Seriously.
FYI, I always bring my own chip scanner. I scan the dog before I start out, and have my reader as back up in case the animal control reader isn’t working, or the officer can’t find the chip. Had a few harrowing moments - but the border officer has always accepted my scanner when his or hers didn’t find the chip. A scanner can be bought inexpensively at Amazon.
A new four footed friend - how exciting! Wishing you and your family all the best.
Literally head over the border with the dog, have a coffee, turn around and head back in after declaring him. Luckily we didn’t get checked on the way out, and it was (relatively) trouble free… but I live in a small gemeinde where the (only) vet deals more with sheep than dogs so he’s used to doing things his way 
