Private Girls Schools North Sydney

We are moving from New Zealand to North Sydney early next year and wish to get our daughter into a Private Girls School ready for the new school year. Our concern is the time needed on waiting lists before entry and whether or not Private is even an option given the fact the new year is fast approaching. Is there any schools that you know of who may have places at short notice? The schools that have come highly recommended are Pymboles Ladys College, Abbotsleigh, Roseville College and Ravenswood. Can anyone give me any feed back on these schools? and experiences on waiting lists?