Hi,
It would probably be correct to assume that your Brother printer is an AirPrint-supported model.
About AirPrint - Apple Support
If so, make sure that the printer and the iPhone are connected to the same network (Wi-Fi router).
Use AirPrint to print from your iPhone or iPad - Apple Support
The AirPrint technology works with wireless (Wi-Fi) or wired (Ethernet) network connections. If the printer has an Ethernet port, you could wire it to one of the LAN ports of the router (instead of using Wi-Fi). This can be especially useful if there is a router-related problem with automatic device discovery and wireless band selection.
Do not use a "direct Wi-Fi" connection from the iPhone to a Wi-Fi network provided by the printer itself.
Also, any change if you try a full power cycle sequence (do not forget the router)?
Power off the Wi-Fi router, the printer, and all iPhones/iPads/Macs/other computers or devices. Wait two to three minutes. Power on the router. Wait two to three minutes. Power on the printer. Wait a minute or two. Power on the iPhones/iPads/Macs/other computers or devices.