I'm pretty sure that's already the case, IIRC. Proof of vaccination or proof of exemption with the QR coded card.
"Vaccine passport" was poor wording from the get-go, and "proof of vaccination" would've probably gone better, IMO. I mean, the latter's existed for decades with regard to admission for school, conditions for employment, etc. and seemed to be far more well received in convincing people to do what's right for the betterment of society as a whole.
As for the shistains who would produce or procure fake passports, they deserve all the ire and punishment that could be directed their way. I am so utterly exhausted of the narcissists on this ******* planet.