Talking isn't really a good judge of intelligence because it is so specific. Males talk more than females do, and you have to teach a bird very specifically for a long period of time when they are young for it to work well.
A better test would be to test some of the basic components of intelligence -
* problem solving
like human intelligence tests do.
So first, memory. That's easy, heck, MythBusters did intelligence memory tests with goldfish. Just show your parakeet a treat in their play area, and then put it into one cup of a cardboard egg holder (i.e. rip an "egg" top and bottom off the set of 12). See if the parakeet tries to get into the egg holder for the treat. Do this once a day for a few days. Then the fifth day put the treat in the cup out of the keet's site and see if the keet is smart enough to try to break into the egg holder anyway, because it remembers the treats are in there.
For problem solving, make a little obstacle course for your keet with cardboard, leading to a treat. Make things she has to go under and around, and see if she figures it out. Like put a treat into a box she can see into through holes but not get into via the holes - and then make a tunnel that leads into the box with a paper towel tube (NOT a toilet paper tube). See if she figures out to go into the tube
That sort of thing is great for intelligence tests