Wow. So much wrongness in one little button.
1) Most Indians consider "squaw" a vulgarism or a slur.
2) The feather, warpaint, and bearclaw necklace are all standard stereotypes for portraying a generic Indian.
3) These stereotypes position Indians as primitive people of the past. No other race or ethnicity gets this treatment. There's a bulldog dressed as Chairman Mao, but that kind of proves the point. Nobody would think of homogenizing a billion Chinese people by calling it a Chinese badge.
4) A female--even a female cat--wearing the trappings of a male warrior would be wrong or inappropriate in many Native cultures.
5) Dressing an animal as an Indian sends the false message that "Indian" is an identity you put on like a set of clothes. That it's a matter of choice, not a matter of birthright and upbringing. Indians are like robbers or superheroes, according to Takkoda; anyone can aspire to be one.
For more on the subject, see Why Thanksgiving Pageants Are Wrong and Chihuahuas Dressed as Indians.