My daughter has people in her class that have November birthdays so I believe your daughter will be fine since she was born on 10/23. If you are unsure, you can call the school directly (speak to the principal or assistant principal). 914-693-7510 or you can e-mail, the e-mail addresses are listed on the website. The elementary school is called Concord Road elementary school.
http://www.ardsleyschools.org/
The elementary school (K-4th grade) has a before/after school program. It's called Ardsley Childrens Center and you can drop off your kids as early as 7:30 and pick them up as late as 6:00. There are several options to choose from. You can do mornings only, evenings only, both, 1 day, 3 days etc etc. There are many different options and they are very reasonably priced. Many parents take advantage of the program, including myself. Here is their website for more info. BTW, area code is 914 since they don't seem to list it on the website, in case you want to call. Meghan is very nice, she can probabl fax you the paperwork with the costs since you have to register ahead of time.
http://www.ardsleyschools.org/elem/PHB/ardsleychildrenscenter.htm (broken link)
Also, keep in mind that Kindergarden has a "phase-n program". They go to school for half a day for the first couple of weeks so the kids can get used to it and then they go full time. Ardsley Childrens Center has a program to accomodate parents during tha phase in period.
Normal arrival/dismissal for K-1 is 8:30-2:50. Dismissal is at 2:20 on Wed. For 2-4, its 3:10 and 2:40 on Wed.
There is bus service as well.
Hope this helps.