You must have already checked that, but just in case, under Safari > Preferences > Passwords make sure that that the AutoFill user names and passwords checkbox is selected.
If it does not work and you are using iCloud Keychain :
On the official Apple Support Website, there is an article about Troubleshooting iCloud Keychain. Here is what it advise you to do :
First make sure that your device is currently on a Wi-Fi or cellular network. If the connection appears strong, try these steps:
1. Turn off iCloud Keychain on all devices.
2. Enable iCloud Keychain on the device that has the most up-to-date
3. Enable iCloud Keychain on your other devices. They will be updated
with your new iCloud Keychain.
When you enable back iCloud Keychain, DO NOT FORGET to do it — as explained by Apple — on the device with the most up to date version of you list of passwords (in your case it must be your MacBook Air).
Hope it helps.