Unless your FTP session has means to unpack, say, a .tar file, I think you're kind of SOL. Perhaps your web admin would be receptive to installing the module for you? Maybe he'd be receptive to unpacking a .tar file for you? Bundle up the installed XML::DOM (or perhaps just a subset of things in your perl5 lib directory to be sure you get enough Perl modules that XML::DOM will require).

If you're really really desperate, you can probably go through and manually build a perl lib directory with FTP commands, putting each of the files XML::DOM installed. This is assuming that the target OS is compatible with the source OS. You might be able to write a Perl script to do this for you, and even then there's no guarantee it'll work.

Another option might be to use RPC somehow and Storable with a 3rd-party system that is more flexible with the stuff it installs. Have your CGI execute a procedure on a remote system to do all the weird parsing stuff, and have the remote system return data structures that represent the results. This is, in my opinion, a relatively horrible way to solve your problem, but it is a way.