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Yes. Internet recovery will work. Format it in disk utility inside internet recovery and install as normal.

If you want you can also prepare a full macOS installer usb in advance but it’s not a strict requirement.
 
Is the MacBook Air an Intel-based Mac?
Or... does it have an m-series CPU?

Does she have a backup drive?
That would make migration of "her stuff" from old to new much easier.
 
"It's Intel and there is a TM backup. Can MacOS be installed migrating from that?"

I've never used TM, so I don't know if a tm backup can completely restore an Intel-based Mac, including the system, etc.

But...
I DO know that you could:
- boot to internet recovery
- get to the internet utilities and open disk utility
- BE SURE to go to the view menu and choose "show all devices"
- the internal drive should be the top item on the list on the left
- erase it to APFS, GUID partition format, then...
- quit du and open the OS installer. I'd accept whatever version of the OS it offers.
- install a fresh copy of the OS on to the drive
- when you see the initial setup screen (choose your language), connect the backup
- now, when setup assistant asks if you wish to migrate from another drive, YES, do so
- "point the way" to the tm backup and give SA time to "digest everything"
- SA will present you with a list of stuff to migrate -- I'd just accept it all and let SA do its job
- when done, she should see her login screen, just as before.

Good luck.
 
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