It'll be better if you don't move from 12.04 to 13.10 directly. The package scripts are responsible for conversion and creation of new settings which will be messed up if you jump releases like that. You may end up with a buggy system that'll ruin your experience with the new release. It'll be better if you upgrade to 12.10 and then to 13.04. The releases are made that way so you can go from one version to another or from one LTS version to another LTS version.
When you've got 13.04, you can further upgrade to 13.10, but I'd really not recommend that. It is still under development, and is not suggested for regular use.
If you do wish to use 13.10, my suggestion would be to download the .iso of the file from here, and boot it from a LiveUSB or on a virtual machine on Ubuntu itself. VirtualBox is a great tool for this, and you can run 13.10 without the risk of your system crashing and consequent data loss.