First of all, the style comments are useful and correct, and would help. However, if you need to process 1.5Gb of XML, you're going to need to manage memory a little bit better.
XML::DOM doesn't automatically free space it used. This is a sign of its age, and newer modules manage memory much better, and tend to do this automatically (I also use XML::LibXML, which does this, and I'd also recommend it highly).
Mainly, you need to call the dispose method to clean out a DOM tree when you have finished with it. This is fairly clear in the pod synopsis for XML::DOM. Just calling it may be enough to get your memory issues resolved. (Technically, DOM trees tend to contain cyclical references, and these are not automatically managed in simple referencing counting garbage collection. Perl has used weak references to assist, but it looks this hasn't been integrated in XML::DOM fully. Simply unreferencing the tree is not enough.)
I'd certainly look to improve style elsewhere. Some other style issues; I'd try Try::Tiny to handle the eval {}, as you seem to be using it mainly for exception handling. Also, several bad experiences have taught me that using a solid date/time parser is always a good idea. I use the ones in DateTime::Format::*. There are many odd cases in date and time parsing, and this will save you lines of code and make the handling more reliable.
