Morning Horent.
Yeah, you can leave your router where it is, it will transmit wirelessly around the house. You will however need a wireless adapter for your PC, as it will no longer be connected to your router via ethernet (network) cable.
You can pick these up for next to nothing these days. (
http://www.ebuyer.com/search?sort=pr...imit=10&page=1)
I would consider the positioning of the wireless router though, it's advisable not to leave them in the corner of a room, or at a low level such as under any sofas etc.
It's likely that you will notice a small degredation in speed / webpage response / loading times.
edit: Before you move your PC to the other room you will need to enable the wireless capabilites of the router (they're usually disabled by default) Obviously the only way your PC can speak to your router currently is through the network / ethernet cable. So, to summarise, you'll have to load up a web-page, access your router from this (it will have an ip address you can just type into the url bar of your browser) from there you will be able to enable the router's wireless capabilites and set a password for your wireless network.
Good luck!