Timna, the best thing is to find out first if the publisher is okay with multiple submissions. That sort of info is usually in the Australian Writers Marketplace (available through the Qld Writers Centre
http://www.qwc.asn.au)or by phoning the publisher to ask the receptionist. Some publishers are fine, others don't want that. The golden rule is to always admit if you're doing multiple submission. Publishers and agents talk amongst themselves, and if one is hot for your book, then she discovers someone else has it and she didn't know... well, you don't want to get a bad reputation in the business before you even get started.
If time is of the essence for you, I'd suggest the Friday Pitch to Louise Thurtell at Allen and Unwin as a first stop. The turnaround there is pretty quick I believe, so you know one way or another where you stand with regard to what that publisher wants.
Let us know how you go. I'm so excited that you're sending your baby away at last
