First of all, they don't get your country. Although they can make a connection between an IP-Adress and a location through Geo-IP databases.
These are fairly accurate with most of the IPv4 Addresses.
Other things to track you are for example cookies and other information sent by your client. Panopticklick lists them in a nice readable form. ( https://panopticlick.eff.org )
Remember, apart from the things your client transmits they only see your IP-Adress and your request.
Yes a Proxy hides your IP from the final destination, but the proxy can still make the connection between the requests and your IP. And for most ISP the IP-Adress is not really uniquely as the assign them dynamically or even NAT all your requests.
So your IP is not really the problem if you want to protect against tracking from a website.
But the bigger problem is that your client still send's a lot of data, which can still uniquely identify you. The TOR Project tackles this problem by distributing a Browser-Bundle which is configured not to send these informations or delete them after restart because some websites need these informations to work properly.
So every Tor Browser looks the same and can't be distinguished after a browser restart.