Yes, they're age based (if administered correctly). One of the test gurus will come along with the details, I'm sure, but all IQ tests compare kids against others in their same age range (with the number of months in a range changing with age).
A reputable tester would not retest her with the same instrument - the results wouldn't have any validity. So she'd be tested with something other than the WASI. (It's possible all of the Wechsler tests would be off-limits due to item overlap.)
As to the gifted-identified kids being older, I suspect that's because they're using an achievement test as a screener, and using a relatively high cutoff on that screener. So you have to have both a high IQ and a high achievement level to get into the program, whereas an underachiever with a high IQ or a high-performing kid who can't demonstrate high IQ would be excluded. The achievement test will tend to select for older / more mature kids, IMHO.
If your school did achievement testing in earlier grades, it's possible your daughter didn't meet the achievement test cutoff earlier, so wasn't considered for further testing.