Hi! Good for your daughter!
For what it's worth, my 27 month old has been very similar with each of these milestones, and I don't see any reason to have him tested. DS1 was given the WISC-III at 3 1/2, but only because our preschool teacher strongly recommended it and we didn't know whether it was important or not. Once we had the results, it confirmed that he is PG, but other than that it didn't make any difference whatsoever. Plus, for a lot of activities where you'll later need testing (DYS, for example), the test has to be administered within a certain frame of time. Testing too early just means we'll have to test again.
We did submit DS1's scores with his kindergarten application for PS just to show where he was at, but they didn't do anything with it at first. (They did come to us on the 2nd day of school and recommend placement testing/grade skip, so if I had to guess, I bet they opened his file and saw the scores at that point.) Otherwise, besides DYS, it hasn't meant anything at this point and he's now 6.
I would keep having fun and encouraging her to explore new things. The 1-1 correspondence is great. What I've learned between DS1 and DS2 is to put any practicebooks away and just explore the world together, focus on social skills through playdates, and keep pulling out puzzles, blocks, and similar "thinking" activities to play together. My DS2 doesn't get nearly enough of that, but I have to keep reminding myself that this is what's most important!
