I’m quite not sure what you mean about testing in Round 1 vs. Round 2 — you can try to receive offers to schools you missed out on the first time around in Round 2, but by that point it’s too late to take the SEES exam. If you want your daughter to take the Classical (and/or Gifted) test for this application cycle, you need to sign up for a date for her to take the Kindergarten Selective Enrollment Exam before the application closes on December 15th. The date you sign up for may be later than that, but you need to actually get your test date scheduled prior to the close of the application. Right now there are dates available from December 17th through January 21st.

As far as when you take the test, there’s no real advantage to waiting (or not waiting) in and of itself. Applicants are scored within age bands (so a child who is 4 years, 5 months will be scored against similarly-aged peers, while a child aged 5 years, 3 months will be scored against a totally different cohort of same-age peers). Hope this helps!