When he arrived, though, he was plain white all over. No problem, there, though: Doodle got his name because he loved to paint! He would paint new patterns on himself all the time, to suit his mood.
When Tootsville I was being created, Doodle was designed as a special premium plush character with a white skin made of a flexible version of a “dry-erase board.” The idea was that his owners could draw on him, then wipe it off.
A few things worked against poor Doodle, or he would have been one of the Basic 8. First, the special plush dolls were going to cost more than double the regular Toots. Second, someone realized that “Doodle Toot” sounded a bit like saying “I thought I was going to fart, but …” in a rather unpleasant way, particularly to Commonwealth (UK/Aussie) English speakers, which was not a great thing. And, finally, the ability to actually change out the patterns and colors of the Toots in the video game wasn't around until Tootsville III or Tootsville IV, so he couldn't be in the game.
His new “back story” makes it all work, hopefully.