Wikipedia describes Anastasia thusly;
[Y]oung Anastasia grew into a vivacious and energetic child, described as short and inclined to be chubby, with blue eyes and strawberry-blonde hair.The source given for the information is the book Memories of the Russian Court by Anna Vyrubova, published in the 1920s. However, scanning through an online version of it I could only find reference to her hair being "blond".
The book also describes her mother, Empress Alexandra Feodorovna, as having "red gold" hair.
Tall she was, and delicately, beautifully shaped, with exquisitely white neck and shoulders. Her abundant hair, red gold, was so long that she could easily sit upon it when it was unbound. Her complexion was clear and as rosy as a little child's. The Empress had large eyes, deep gray and very lustrous.At the moment Russia holds a slight fascination for me. I'm beginning to think it's the most mysterious country on Earth. Then again it may be just another phase of interest I'm going through.