Upgrade exchange 2013 from 2003

Hi,

We currently have Domain Controller (DC) 2003 and exchange 2003. We need to upgrade DC to 2012 server standard and exchange 2013 standard by using CodeTwo Exchange Migration.

Can we install Server 2012 to current DC 2003 machine? Can we do the same for exchange 2003 as installing exchange 2013 on top of 2003? Is it work as software version upgrade?

Advantage: Server name and static IP not change 

Or

Install new Server 2012 machine and Migrate Active Directory (AD) from server 2003 to server 2012. While this process running, will our exchange 2003 still working?

After successfull of AD migration to 2012, Do we need to migrate Exchange 2013 right away? Thanks

Regards,

Truc