Posting this as there wasn’t a clear answer elsewhere online. Brother have not released a driver package for M1 Macs running Monterey and suggest you install their printing app from the app store – an app which has terrible reviews.
The good news is, the old drivers for MacOS 10.15 (Catalina) still work, at least for my HL-1210W laser printer. I’ve tested this on my own M1 Macbook running Monterey. Search the Brother website for drivers for MacOS 10.15 and you can probably get away with using them with your Brother printer.
If your printer supports AirPrint you can just use that – no need for installing drivers.
The driver package I specifically downloaded for the HL-1210W for MacOS Monterey was:
MacOS 10.15 / DCP-1610W, DCP-1612W, HL-1210W, HL-1212W / 27/09/2019 (1.5.0)
Below is a link directly to the installation package on the Brother website. It’s just the drivers, no annoying print tools or any of that.