Probably so. Be sure to check the patch on RT for the `open' method, whose API changed (in Firefox at least). I don't know what Iceweasel/Iceape are, I assume browsers.
If you look in Makefile.PL, you'll see that it basically uses pkg-config to find the location of the libraries/headers of Firefox/Mozilla. You might have to install a -dev package, like you install firefox-dev for firefox; maybe iceweasel-dev. Then add your package to Makefile.PL (sorry it's not exactly cleanly written...)
I plan to release a new version of Mozilla::DOM and Mozilla::Mechanize soon. Thanks to Boris Sukholitko, I can finally run Gtk2::MozEmbed/Mozilla::DOM/Mozilla::Mechanize on my Ubuntu system again (let me know if you have a problem with it segfaulting), so I can finally release a new version. Be sure to check out Boris's modules if you're using Mozilla::Mechanize, in particular for adding the ->success method. (I hope I can integrate that into Mozilla::Mechanize, but for now it's separate.)