Can you plug a router into a router?

I've been lurking here since October '06 and this is my first post. This place is a goldmine that I found about a month before I took delivery on my first ever Mac, a fully tricked out MPB that I'm lovin'.

The only problem I've had is accessing my HP 3600 All-in-one printer that's connected to a PC by USB. I recently switched to Verizon FIOS fiber optics and the router is an Actiontec M1424-WR with 4 Ethernet LAN ports available. It provides 802.11G, but I wonder if I plug an AirPort Base Station into one of the LAN ports I could use the USB connection on the Base Station to print to the HP 3600 from my MBP and maybe bump up the speed of the MBP to 802.11N as an additional plus.

If this is not the proper forum for this kind of esoteric question, I trust someone will let me know, but I want to hear what you guys have to offer since I feel more comfortable here than anywhere I else I could imagine.

I don't see why you would plug one wireless router to another. It won't double you speed if you are asking. I plugged a wireless router to my gaming router d-link 4100 and it didn't double the speed, just increased slightly or so it seemed.

I have a Linksys wired router handling the connection to the DSL modem (Verizon) and anything else which is wired. Connected to that I have a Linksys wireless router which functions as a wireless access point much like an Airport base station. So essentially, I have a router connected to a router. In fact at the moment the only thing connected to that wired router is the wireless router which serves all my computers (two Macbooks and a Dell laptop) that have wireless.

I have, however, disabled DHCP on the wireless router so it's the wired router that serves up IP addresses for everything. The wireless router is assigned a unique IP address under the range of the DHCP addresses, but other than that there isn't much configuration to it.

My reasoning was that if I plugged an Airport Base Station into my current wireless router's 10/100 ethernet connection it would take the speed of the 802.11g (54Mbps) to the ethernet's (100Mbps) that the Airport Base Station could handle plus I could plug my printer into the Airport's USB connection and have wireless access to the printer for my MBP.
Anybody old enough to know who Rube Goldberg is?

Sorry I,m late but I want to try something similar. Walkerj how are the routers connected to one another? via a cable or wirelessly?

Yes, you can plug a router into another router. All routers usually work togather with routing tables, so as long as DHCP is automatically enabled you should be fine.

Can this also be done wirelessly? (sorry i'm a bit of a dunce when it comes to networks)