9grams,
It’s very rare for a WordPress database to approach the 1GB size limit unless you’re using a plugin that stores large amounts of data in it. I’ve seen this happen with some stats plugins, but there are alternatives that don’t store the info in the database. I recommend researching WHY your database is that large and fixing the cause rather than looking for a way to store such a large DB.
For the record, there isn’t currently an option to increase the storage available for a database when using Go Daddy’s traditional hosting plans. If you’re unable to stop the database from growing beyond the allowed size, you’ll have no choice but to find another solution (like a virtual dedicated server, fully dedicated server, or virtual datacenter).