Hi Qwerty.
My daughter will be 4 next month and we haven't tested her beyond the school tests they administer to the students. My DD goes to a Spanish Immersion program which is academic and 2 years ahead of the public schools. We didn't have to test her to get her into the program and would have been the only reason we would consider it at such a young age.
Reasons why you shouldn't: The tests don't give the most accurate results at a young age, plus the results would not be valid after a few years and you would have to retest her spending more money. The age range they claim to be the most accurate for testing is around age 8. We plan to test DD when she is around 7 unless we find that the school is not working for us anymore and need to figure out another solution.
Also, just in case you haven't read about potty training and the gifted: a lot of gifted children will be slow to potty train. It sounds like you are doing a wonderful job with introducing her to it and not pushing her. My DD was one of those that I was ready to pull my hair out because she out and out refused to potty train. We tried the reward system but she could care less. Even bought her this beautiful dollhouse that she begged for and left it in view for her to see. Yep, didn't excite her enough to really try. She decided when she was ready and when she made that decision she was potty trained (night and day) within 2 weeks. She was potty trained in 2 days for pee pee and a week for poop. Another week of more me not sure if we should take it to the next level and she was potty trained for nighttime. So if she takes her time with it don't get discouraged. She will eventually decide she is ready.
