I'm late to this one, but DS won't be 6 until December. He was tested in August (he started K in August)and is in 1st now. He's doing SO much better all around and will start a gifted pullout in January. His school tested him using the Iowa Acceleration Scale, so it wasn't just based on his achievement tests. We did not pay for private testing.
And fyi, if your DD is "immature" with you, she may not be once she is in school AND in the right environment - I was shocked b/c DS's school said he was super mature, which he's not with me. He's made friends with ease and still plays with those he made in K as well (recess/after school when he's in ASP, etc).
Oh, and my brother was a Sept birthday. At the time in NJ, there was no birthday rule. When moving to GA, there was. So he was a whole year younger than most of his classmates and did fine.
Personally, for us, it was a must do now with DS - before he learned to take the easy route and stopped enjoying learning. We'll cross the middle school and high school issues when we get there.
And I think the birthday cutoff is a crock of (scuse my language). I think it itself is the one thing that causes so many issues with kids in K and 1st! My DD4 has to wait until August 2011 to be in K, yet she could've easily been in the state funded pre-K here this year and move to K next year (and we're pretty sure IF she is GT, it's very, very mildly - DS was academically far beyond where she is now at her age).
Anyway, I'm babbling in circles, so I will stop.
Good Luck!