International travel is going to need a lot more than a simple vaccination card.
There are already a couple of more-secure proofs of covid vaccination being trialled, for this purpose.
One Potential Method of Proof
... the international airline regulator confirmed it was in the final development phase of the IATA Travel Pass, a digital health pass designed to support the safe reopening of borders.
When international travel opens up, this is why I'm flying with Qantas
Iata is working on a digital platform that will allow passengers to prove their tests and vaccination results “in a verifiable, safe and privacy-protecting manner”.
‘Digital Covid passport’ linked to vaccine could revive travel
Another Potential Method of Proof
A similar concept has already been trialled. The CommonPass is an initiative of The Commons Project, a Swiss-based non-profit social enterprise. With the aim of restoring confidence in travel and returning global travel and trade to pre-pandemic levels, the CommonPass verifies a traveller's health status via a smartphone app.
When international travel opens up, this is why I'm flying with Qantas
ETA: Also, Singapore has something called an Air Travel Pass which allows entry to Singapore for people from low-risk locations (Australia, Brunei, Vietnam, New Zealand, China) to make short term visits to Singapore, with certain PCR test stipulations.
Lessons Australia could learn from Singapore's international reopening