You've already paid for (at least) a year of domain registration. Once you change hosts, you can edit the WHOIS info for your registration here to use the DNS servers at the other host. Registration and hosting are two separate systems. Kinda like your drivers license and car registration. You need both, but they're not necessarily done at the same time and at the same place.
Before you do that, take a screenshot of all DNS settings for that domain here in the panel by clicking on Domains -> Manage Domains, and then the DNS link. You'll need many of those entries at your new host site if you want to use Gmail.
Those DNS entries do two things: One is that it tells your web browser where your webmail interface is, and the other is that it tells mail servers where to deliver your mail. Ok, three things: it tells your mail client where the POP/IMAP/SMTP server is.