Allah is the same God followed by the Catholics/Christians and Jews. So in truth, you are not praying to a different God. It is good to pray on time but there is leniency if you are unable to pray at the exact time of the prayer, as long as you do it as soon as possible. I don't remember the exact limits of how long you can wait before praying or if you can pray them earlier if more convenient. I am very new to Islam myself.
If your lunch or spare period in the early afternoon works, just find a quiet corner and do your prayer. If you are 'caught' just say you are praying to God. Allah is the Arabic word for God basically. Or, you can just talk to your teacher/principal and tell them you are a muslim and would like to have 10 minutes to pray in the early afternoon and a place to do it. They may allow it, simply because you asked. If not maybe they will expel you and you can go to a public school instead or one more tolerant to Muslims.
You can also check the Board of Education website/rules for Catholic schools in Australia in regards to non Catholic students...I am from Canada and I did go to Catholic school from kindergarden to grade 8, no Muslims there but there were Jewish students and their holidays etc were honored. (basically they were excused to take different days off and from participating in the Catholic rituals in school). This was quite some time ago to.