There isn't a simple "change this domain" button to press. There are, in fact, a multitude of considerations.
Looking only at the Active Directory implications your best bet is to approach this as an Active Directory migration. You would use a tool, like Microsoft's Active Directory Migration Tool (ADMT) to migrate all the accounts with mailboxes out of the domain hosting the Exchange 2003 server into the domain with the Exchange 2007 servers.
If your concern is physically re-using the Exchange 2003 machine then you're going to need to perform a multi-step migration wherein you move the mailboxes to a "surrogate" machine at some point so you can free-up the physical computer running Exchange 2003 and rebuild it as an Exchange Server in the domain hosting the Exchange 2007 server.
There may be client connectivity issues. Think about name resolution and packet flow for MAPI and other types of clients. If you're using Outlook Web Access you may be looking at firewall rule changes.
There are mail flow considerations, too. You need to think about how Internet and internal email is going to continue to flow as you make these changes and how the existing Internet address space is going to be handled.
Given the nature of your question it's likely that this isn't something you have a lot of experience with. You may want to consider getting an experienced local Exchange consultant involved so as to maximize the speed and efficiency of your migration.