I have the same issue I've been thinking about for years. I haven't used Earthlink for my internet service provider in a very long time, but still use that email address, for which they charge me a somewhat nominal fee.
I see in the webmail preferences, under "General" there is Email forwarding, which allows you to have all incoming email forwarded to a different address. So that might help you.
I don't know how to move existing emails over other than to open and forward each one to your new email address.
In preferences you can also export your contacts in csv format. Then maybe you can import them into gmail.