Sidecar works, but buy a monitor.

You can, but I wouldn’t rely on it as a permanent setup.

Apple’s Sidecar lets you use a MacBook Air as a second display for another Mac, but it has caveats. Both Macs need to be signed into the same Apple ID, on the same network, and running recent versions of macOS. The Air has to be an Apple Silicon model or a 2016–2019 Intel model with Sidecar support. If you’re using a Mac mini with an M-series chip and an older Intel MacBook Air, it might not work at all.

Even when Sidecar works, latency is noticeable—especially for dragging windows or watching video. You’re also locking up your laptop; you can’t use it as a laptop while it’s acting as a display. Third-party apps like Luna Display or Duet Display exist, but they cost money and still introduce lag compared to a real monitor.

If you only need a secondary screen occasionally (say, for a quick code review or extra reference window), go ahead. But if you plan to run this setup daily, drop $150 on a basic 24‑inch monitor. It’ll be faster, simpler, and free your MacBook Air for actual portable use.

Your Mac mini deserves a proper monitor.