Unfortunately I don't have any experience with yum. I use Ubuntu and the PHP compiled for it (and probably all debian based distros) have DOMDocument by default. PHP version is 5.3.2 but as far as I know XML support had major changes on PHP only from version 4 to 5. So I don't think that your problem is that you are running 5.1.6. Nonetheless it is a good idea to check that.
I was unable to find in which PHP version DOMDocument was added. If you find this information please let me know and I will add it to the documentation.
I can't say if you have XML support enabled. Apparently yes but this --disable-dom seems to state the contrary.