Is Roo from Winnie the Pooh a fairy tale character?

Not technically. The Winnie the pooh stories by A. A. Milne were written and published in the 1920's, making them Classic Children's Literature. They are generally considered too recent to be traditional "Fairy Tales", and the plots of the stories don't fall into any of the standard fairy tale types. (i.e. no royal characters, no epic quests, no romance, no horrible fates for people who don't listen to wise women...)

Like most of the Winnie the Pooh characters, Roo is based on a stuffed toy, in this case a baby kangaroo, owned by A. A. Milne's son, Christopher Robin Milne.