Should I use a router only for QoS and Security purposes, when I don't have more than one computer?
If you are connected to the outside world (i.e. you have internet access), you should own a router.
The security benefits far outweigh the small cost.
Besides, it's very cool to sit on the couch in the living room with your laptop, tablet or phone (if you have one or are going to eventually purchase one), and have wireless internet access.
A cheap router isn't much more expensive than a cheap modem, and the security benefit of having a hardware firewall is well worth it. I imagine the Windows Firewall can be configured to make your computer as secure, but I wouldn't bother. Especially if you install software that adds itself into the firewall, that port is now wide open for the internet to see.
With a router, unless the program is using something like UPnP then your PC is still just as secure.