Definitely check out The Harbourside in Kowloon Station. One of the best playrooms for kids in town, beautiful views and the whole area is is very kid friendly with nice outdoor playground, skating rink etc. Extremely conveniently (Wanchai 20min max., Central, Mong Kok) located and lots of kids here take the school bus to AISHK which takes app. 30-40 minutes. Till that time there is a great
pre-nursery/kindergarten within two minutes walk, PIPS. Would suggest you sign your daughter up asap though. For your budget 3bdr is easily doable. Good luck, you can pm me if you want more info!