I am unclear from what you have said how the printer is connected. Is it
connected to the XP computer by usb or to the router by LAN? In the former
case you will need to install and setup Samba. In the latter case you will
need an IP address and the printer will need a built in print server.
Setting up a printer by IPP is easy as long as you have the static IP
address. My Brother laser printer is connected this way and it works great.

The fact that it works in XP is immaterial. What you mean to say is that the
printer is working because it prints from XP. However, that does not mean
that it will automatically work in another OS since most printers are made
to work with Windows and it likely shipped with a Windows driver. Linux
support is hot or miss. Depending on the printer, drivers may or may not be
available. This has to do with whether they are open sourced by the OEM,
whether the manufacturer supports Linux or there has been enough time to
backwards engineer a driver. If it is uncommon printer then it may never
happen. Fortunately Brother is commonplace and Linux drivers are available.
If you use Synaptic then you can do a search for brother and it will show
you the drivers and the printers that driver supports. If you use Software
Centre then you are on your own does not provide as much information.