libxml2 is not by itself a Perl library. XML::LibXML is simply a wrapper around the interface it provides. Therefore, you must install libxml2 to your system first. Your command lines suggest the usage of GNU/Linux. If this is indeed so, then you can use your distribution's package manager(zypper, yum, apt, or others) to quickly install libxml2. In your case, you should ask your system administrator.
If no such system is available, then you must download the sources from their website. Then, when running the configure script, specify --prefix to be somewhere in your home directory.
That possibility was already hinted at in the dump you provided. You might want to read it, you know. ;-)
"Excuse me for butting in, but I'm interrupt-driven..."