The purple squirrel is actually a subconscious manifestation of Reggie's daemon.Word of God has stated that the squirrel is Reggie's voice of reason, his conscience. In the first chapter, almost the first page, of The Golden Compass, we see Pan telling Lyra that she should not be in a certain room. Perhaps the Disney worlds, stated to be arranged around the parks like the spokes of a wheel, are actually distinct universes, in and of themselves, but the barrier that separates them is so thin as to be nonexistent. And Reggie, who, as we know, is "not always all there", can use more of his brain all at once, to subconsciously bring his daemon from another world where he has one, to our world. A squirrel daemon would suit him perfectly. Squirrels tend to be easily distracted, and then focus on one thing to the exclusion of all others. They also have large front teeth, just like Reggie. Why purple? 'Cause it's Reg.