There's no detailed standard as to what's required for non-residents of Quebec. The QC government just says "Official proof of vaccination against COVID-19 issued by their country or province in Canada", so ultimately it will come down to the person at the door reviewing your documentation.

I suspect a photocopy of a CDC card should be satisfactory to most, if not all, establishments. A friend of mine who was vaccinated in the US showed something on his phone and it was fine, and I've had no problems with a printout of my Alberta provincial health records. A friend from Ontario showed something on his phone.