Our biggest clue was at our 4 month well-baby visit when the pediatrician couldn't stop raving how DD was the most advanced baby she'd ever seen.
Some of her major milestones were:
Smiling/head control/alertness almost immediately
Repeating "hi" somewhere between 4-6 weeks old
Turning pages in her books/pushing buttons in her electronic book to play songs at about 3.5 months
Sitting up for extended periods of time alone at 3.5 months
Crawling backwards at 4.5 months
Taking first (assisted) steps at 6 months
Has a vocab of 3 words at 6.5 months (up, eye, hey)
Can sign about 5 words at 6.5 months and has some other gestures she's made up to get her point across
Now at 6.5 months some of her favorite activities are playing with building blocks (mostly she just knocks them down still...), pointing out facial features to get their names, practicing walking, taking out and putting back in the numbers in her floor mat, having books be read to her with an insane intensity, playing peekaboo where she removes a cloth from her face or my face, and posing for the camera.
She's way too young to be tested but since DH and I were both gifted growing up and most of the things she's doing are just too obvious to ignore we have our suspicions.
