Computer Help and Support

You could try to scan the QR code image that's now on your phone with another phone/tablet/etc.. The other phone would need a scanner app that reads QR codes.

If your test fails, you might want to get a better QR code image.

If your test succeeds, that's a good sign. It's not a guarantee that the airport's scanner will read it, but it's a good sign.

A paper copy, backup or primary, is a very good idea.

On edit,

I didn't read the OP very carefully. You took a picture of the QR code displayed on a laptop? Could you possibly transfer (copy, email forward, usb drive, etc.) the email from the laptop to your phone? That way you'll have a digital copy on your phone, with the same quality as the original.

You can still test as I mentioned above.