Generally speaking, the home router ONLY cares about the protocols going between your local LAN and the Internet. Stuff that is moving around inside your LAN is just passed along. That is to say on the local LAN side of the subnet the router acts as a switch and not as a router.
But routers will NOT pass Bonjour protocols to the internet. Bonjour is a subnet ONLY protocol so routers will not pass Bonjour to another subnet.
If you have 1 and only 1 routers in your home, then chances are Bonjour is going to travel around just fine. You can use a utility such as Bonjour Browser to see if your Mac sees your printer.
<http://www.tildesoft.com>
or
<http://husk.org/apps/flame/>
Where you can get in trouble is if you have 2 or more routers in your home, and the extra routers are NOT configured as access points with all their router functions turned off. The Apple term for this is "Bridge" mode, other router vendors call it something else.
For example if you have a router from your ISP, and then you put your own WiFi router on that, or you get a Time Capsule (which is also a router) and some devices connect to one router and other devices connect to a different router (either via ethernet or WiFi). Each router is going to create its own subnet and Bonjour will not cross into another subnet.
If this is the situation, then you need to configure the extra routers to turn off their router functions, and become just WiFi access points.