In almost all cases when ./configure halts with an error that some headers and/or libraries are missing, you need to install the *-devel rpm package for whatever it is. In this case, it's a matter of:
yum install qt-devel
The previous halt on the missing X headers wasn't as obvious as to what package to install, as 'yum install X-devel' would not have worked. Sometimes you have to figure out the actual name of the package to satisfy the missing dependency. In the case of the missing 'X' headers, I didn't know the answer myself, but I knew how to solve the puzzle.
Code:
sudo yum list *x* | grep devel
Near the top of the list returned, it was fairly easy to guess that libX11-devel was the most probable package. You'll no doubt hit other dependency issues before you have them all on hand. Learning to become somewhat proficient at using yum at the command line to find packages will go a long way in assisting you when compiling software and gathering up the required dependencies.
Edit: And when that didn't satisfy ./configure, then 'sudo yum grouplist' made "X Software Development" the next logical choice.