There is no minimum age for boarding at our Sitter's homes. However, you will need to communicate to the Sitter that until your Puppy / Kitten has had all their vaccinations they have not yet developed much immunity to diseases, it is recommended that they stay away from other vaccinated and unvaccinated dogs or cats (until 14-16 weeks of age).
This means you need to ask the Sitter whether they are ok to have a solo booking (ie. not accept any other booking requests for the time your puppy/kitten is staying with them).
The Sitter can lessen the risk by only taking your new pup or kitten to places that you know are safe. The Sitter should stay away from public parks or areas where you know that lots of dogs defecate. The pup/kitten will have decent protection within a week of the second vaccine (likely given at 10-12 weeks of age), and very good protection after the third vaccine which will be given a month later 14-16 weeks.
Diseases such as parvo virus can linger around in the soil up to 12 months after an infected dog has been there.