Because the version difference is pretty big (in terms of Magento), I would definitely setup a “staging” area where you can attempt to upgrade a non-production version of your store.
What you would do is, setup a subdomain or subdirectory on your domain, like staging.yourdomain.com. Then, install the latest version of Magento. Next, you would copy your theme directories, media folder, and local.xml file over (with updated database settings). You would then create a MySQL dump of your production store and import that to a clean database for the staging site.
There’s a wiki article that will tell you exactly what folders need to be archived and moved over, it’s written for moving Magento from one server to another, but it would apply here as well. Here’s the link:
That way you can test things out and see if it works or what errors come up so you don’t potentially mess up your production store. If all goes well, you can either move the staging store in place of the production store, or do the same thing over again without setting up a staging area.
Just a note, you should always create a full site backup before performing any type of upgrade or move like this.