I haven't tried this but here's an idea.
The Font Thing saves your collection info as TFT files (I think that's just short for The Font Thing). You could copy these files from one computer to another and then help the second computer find the collection info by going to View> Options click on the General tag and make sure that the Collections folder is where you put the collection files that you moved over to that computer.
Now I have now idea how well this would work or what would happen is your 2nd computer doesn't have all the fonts that are in the collections, BUT it sounds like it would be worth a try.
HTH!