Hello justabaldguy!
Firstly, since this is a brand new router, go to the router setup page (usually something like 192.168.0.1) and make sure that there are no firmware updates from the manufacturer, this is sometimes solve the problem.
Secondly, can you please try changing your router's SSID to something new, as some computers and printers will have a conflict with the exact same name.
Usually with routers that have a 5 GHz and a 2.4 GHz network, it does not matter if the wireless printer is connected to the 5 GHz or 2.4 GHz, devices connected to both bands will be able to print, since they go through the router.
But that is assuming that your printer AND router are both AirPrint compatible (which is required for your Mac/iPad/iPhone/Apple Devices).
Let me know how things work out. Good luck!
Edit: Also, while you're in the router setup page, look for a setting that has to do with "AirPrint" or "Printers."