I was able to install and run Firefox 2.0.07 on my Puppy.
On the desktop, there is an icon for PET install. Click on that, and click on the bottom button, Puppy Package Manager. I looked for Firefox, under Internet, and selected it. It showed no missing shared libraries and no missing dependent packages.
After installing, I had to reboot to run it from the menu. Remember that I have a saved Puppy configuration on a flash drive.
The first time I ran Firefox it asked me if I wanted to import my bookmarks from Netscape/Mozilla. I clicked Yes and all my bookmarks were imported OK. (Not the passwords or add-ons, though)
I am digging through the Puppy forum,
http://www.murga-linux.com/puppy/index.php,
to find out more on installing packages from Debian repositories.
That is a promising path to explore.