The conditions are:
- Note from a licensed health-care provider in Canada stating that the inoculations is medically necessary
- proof from the licensed US vaccine provider of a possibly to be vaccinated
The quarantine regulations currently in place have an exception for essential medical services obtained outside Canada. A Covid-19 shot would fall under that definition.
This exemption is in place for people within driving range of a border State that has ample supply of vaccines and it poses a simple way to get vaccinated quicker than what is possible in Canada.
Be aware though that this medically necessary trip would not permit someone in the States to do anything else while outside Canada. Shopping or other actives are not permissible.
The trip has to be in a private vehicle (so no taxis or other hired vehicles can make the trip for you). You can bring a support person to assist you.