Macs often have problems with network routers. You might want to buy an Apple certified router. I'm not an expert on getting Macs to work with routers that aren't confirmed to work with Macs, so I don't know if your router is supposed to work with them fine and I don't claim to know for sure if it should be replaced or not, but it might be necessary.
Also 192.168.1.1 is simply the router's IP address on your network. That's the usual IP address for devices that share internet to other machines on their network if I remember correctly. It doesn't refer to anything special about the router.