Your fob is from 1908. William Howard Taft was the Republican candidate for President that year, and he was running against William Jennings Bryan. He was Teddy Roosevelt's hand picked man to run for president while Teddy left office so he could go hunting in Africa. While he was out of office, Taft made some changes in things that Teddy had done, and in 1912, when Teddy came back and wanted to be President again, Taft wouldn't step down. Thus Teddy formed his own party, the Progressives, and used the Bull Moose as the Party Symbol. He ended up dividing the Republcian vote, and came in second to the Democrat, Woodrow Wilson. Taft came in 3rd. He eventually ended up where he really wanted to be, and that was the Supreme Court. Your item, if it had been perfect, is in the $25 to $30 range. Dug items are worth about half that. If I can find some of my pictures, I'll post a picture of a good one or two.
The photo that I've attached doesn't show your fob, but a mate (Bryan & Kern), along with several others. This will give you some idea as to what a good one should look like. The ones with pictures on them are worth considerably more.