Brother laser printers are great. As long as you get one that supports Postscript (Brother calls this BR-Script), PCL5 or PCL6. You can see this under the “emulations” printing specs on a printer model page. PostScript and PCL both have fully open source implementations so you’ll usually be able to just use built-in CUPS gutenprint or foomatic drivers. I also recommend ethernet (wired or wireless) and not usb.
Do not get one that only says “GDI” emulations which is Windows based and can be really painful to deal with.
I’m sure its just hidden in all that fur. The dog will be okay.