Yes the sooner you can get your child on the waiting list the better. Unless you have an old boy/girl who either provides a recommendation or is related to the child, it can be very difficult to get in at short notice.
On the fees, they will usually charge a deposit when you enrol, which is generally not refunded until you leave the school. On top of that, they will also charge a a one-off fee when you accept the place.
I don't know much about West Australian private schools but to give you some idea of fees, my alma mater's current fee schedule is $1,000 deposit on enrolling (you never really get this back because the fee to join the old boys' association is usually equal to this) then $6,600 no refundable fee on acceptance of place and then school fees which start at $16,000/annum for preschool and go to $28,000/annum for year 12 (significantly more for boarding). Plus there is uniforms, camps, music lessons etc which all add on to that. And they do ask for donations on a fairly regular basis.
You might want to check out the
MySchool website, which is provided by the government and has a wealth of info. Of course with any school, the best way to see if it's a good fit is to actually go to it.
I worked with a guy who went to Christ Church, he had nothing but good things to say about it.