IIRC the Air has a fairly low-res display (1440x900) but can drive a higher resolution external display, so you'll see a useful bump in the number of pixels if you go that route.
Full HD monitors (1920x1080) are cheap as chips these days, but you might like to jump up to the next level and go for QHD (2560x1440), this looks like good value for money:
https://www.amazon.co.uk/dp/B074MMR1V3
Do check on connectivity though - I think the Airs are light on ports, the monitor above has a DP connection which may plug straight in.
Dell make some decent monitors, this one also has an IPS panel which will be nice if your daughter's doing graphics type work but not so good for gaming..
Cheers,
Plug