In the order in which the following media reports were published, she was
- Twelve in September 2011 [quoted by Israellycool from an Arab source];
- Eight in August 2012 [Source: +972, a far-left Israeli site];
- Thirteen in December 2012 [Source: TimeTurk News and other Turkish sources];
- Ten in December 2012 [Source: World Bulletin];
- Thirteen in June 2013 [Source: Your Middle East];
- Twelve in February 2014 [Source; The Guardian];
- Fourteen in September 2015 [Source: NBC News];
- Sixteen in February 2017 [a South African source].
So depending on which media report you want to believe, she was born (in the same order as those links above) in 1999, 2004, 1999, 2002, 2000, 2002, 2001 and 2001.
Making her now thirteen, fifteen, sixteen, seventeen and/or eighteen.
It's hard to be precise. We assume all this vagueness is intentional and part of the family's manipulation of her appearance, her image and her life.
UPDATE January 1, 2018: We tweeted this evening [here] that the Tamimi girl is now 16 years and 11 months old according to the Israel Prison Service, quoted today over at JewishPress.com We think this emphasizes how, since the age of 9, she has been the product of her clan's and parents' inputs, cynical manipulation and child abuse.