My guess is around 4 or 5, but I don't know if it's right because she looked a bit older. So how old was Korra when she was discovered she was the Avatar?
Korra is confirmed to have been aged four when she demonstrated her multi-element bending skills to the judges in the first episode, according to the Legend of Korra: Book 1 – Air, The Art of the Animated Series artbook.
Obviously she's had a little time to work on these skills, so presumably she was three or four when she made the discovery.
"I'm the Avatar. You gotta deal with it!" Ryu wrote a version of the dialogue on one of his early sketches of young Korra. We loved her perfectly it summer up her attitude and personality and incorporated it into the first episode. Four-year-old Korra design by Ki-Hyun Ryu."
Youthful Korra, earthbending and using her strength
Korra: "I'm the Avatar. You gotta deal with it!"
Given her apparent age, her sentence syntax and structure, I would put her age around six or seven in the image above. Given she was likely bending for a bit before that, she may have started as early as five.