hi.
You don't have to upgrade it.
You just need forest and domain funtional level at 2003.
Open Active Directory Users and Computers, right click on your domain and then select Raise Domain Functional Level. Then check the "Current Domain Functional Level" and make sure it says you are on Windows Server 2003.
Then open Active Directory Domain and trusts, right click on your domain and then select Raise Forest Functional Level and make sure it says you are on Windows Server 2003.
And also you need to prepare your domain for new schema by running adprep utility. The command adprep is located on your Server 2012 disk under the \support\adprep directory. You will want to run the command adprep /forestprep from one of
your Server 2003 Domain Controllers.
And it is better to have all recent updates installed.