Dark,
I would email in the first instance. Registrars will be fielding lots of calls. No need to tell them anything they already know, but say you feel it is the right school because she has always been comfortable academically (in the top third of her class or similar) enjoys learning, mention easy transport, friends going either from previous school or brownies etc. Read the website carefully and suggest she is a "taker-parter" in music, sport or whatever. Be positive rather than gushing. Ask about the chances of the list moving.
Then speak to her current school head on Monday. If they send a number of children to SHS they should be able to make a call confirming "this one is alright". SHS want a stead flow of good applicants from feeder schools, so should listen. If it is a prep, getting them to an appropriate next stage is something you are paying for, so you should expect help. SHS are more likely to be open to them than you.
Then hold fire. My guess is that SHS, having recently expanded, may be erring on the side of caution, as they wont want to have to add a bulge class. In about a week or so they will know whether the list is moving. From then on in it is not about your child, but about other people's decisions and tactics. If they think they are going to need to go to the wait list they will encourage you to wait. If things look tight they will probably tell you.
Then phone the day before the deadline for acceptances. Depending on whether it is before or after state school places are announced they should be able to give you a much better steer on whether it is worth holding on.
The next movement will be just before the start of the summer temr when people, still sitting on the fence deciding on a state or indi place, need to pay a terms fees. If you are willing to lose a term's fees your chances of getting a place then should be good.
Most registrars are approachable. Their job (mainly) is to sell the school and ensure places are filled. Keep checking by phone or email every two weeks so they know you remain interested. As time goes on most people on the WL will have made other arrangements, so a place is most likely to go to someone they know will take it.
Lots of people get in through wait lists. Though obviously it is a horrid wait and important to remain as emotionally detached as you can.