The JDK's should be upward compatible, i.e. you should be able to compile your source code written for 1.1.8 on 1.3 without problems.
Just try to compile it. The compiler will maybe give a number of warnings about using deprecated methods. Check all the places where the compiler gives this warning, look in the JDK documentation why the methods are deprecated and replace them by newer methods.
This document: http://java.sun.com/j2se/1.3/compatibility.html explains about the differences in JDK 1.3 with older versions.
Good luck,
Jesper