1 GB is going to be slow no matter what. If you have enough memory to load the document entirely in memory, then XML::LibXML will be the fastest option. If you can't load it and you need to use SAX, then performances drop dramatically (as mentioned previously, look at this benchmark). I am not sure the pull interface is available from the Perl module, but that might give you XML::LibXML speed without having to load the whole document (I have never used it myself, so I am not sure if that's even possible). XML::Twig would be a better option than using SAX. And indeed, XML::Parser might be your best bet, even if it's not the easiest module to use.

Beyond that, you get into dangerous territory: format the XML properly, get rid of potential comments, CDATA sections, PIs and entities, and use regexps. I would try the other options before though.