Assuming that CUPS is enabled on your system. It appears that there isn’t an already created PKGBUILD in the AUR for that printer. I have had good luck creating Brother install files from either .deb or .rpm by using the following guide:
We’ve got a Brother printer at home. I temporarily switched my Manjaro machines from Budgie to KDE, but they had issues connecting to the printer. When I switched back to Budgie, I had no issues reconnecting. It’s something specifically about Plasma.
Have you connected your brother printer through wifi? If so, please check if the packages for the dns-sd function have been installed, such as gvfs, gvfs-afc,gvfs-goa,gvfs-mtp,gvfs-nfs,gvfs-smb, and so on. And then please make sure the avahi service has been turned on.