I already have Google-Authenticator on my iPhone - yay!
I want to have it on my iPad too (which I don't carry with me daily). I cannot see how to set that up in Google's online advice.
I don't want SMS as second factor because it is not in any way safe in 2017. SMS as a second factor is less secure than a strong password alone.
Go to https://myaccount.google.com/security/signinoptions/two-step-verification on your Mac/PC.
Generate, and perhaps print off some "Backup Codes"
Log out and log in to test one of those ten backup codes (perhaps a different browser so that login requires the second factor).
On your iPhone, delete the line in Google-Authenticator for the existing Google-Accounts setup.
Click on the pencil icon, to the right of the "Authenticator app (Default)" you already have.
Click "Change Phone", and show the new QR code the screen. In both iPhone and iPad scan the QR code. Yes, the same QR code twice. Note now that the one-time-passcode is the same on both. Do both quickly as there is only a certain amount of time to complete this in.
Note: I could not find a way of deleting the backup codes. I mean I can shred the printout, but can't see how to get the list of second-factors in Google-Accounts to drop the backup codes.