It depends whether the JQ flight is domestic of over to Australia. If the latter, I believe they will be interlined. If not, the OP will have to collect the bags, clear quarantine, and pass them to JQ.

As noted, JQ should honor your ticketed allowance. If you're over the ticketed allowance, it is MUCH cheaper to pay for the extra weight in advance than at the airport, and you have to somehow know the exact weight of your bags (within relatively narrow ranges), not just the number of bags, in advance. It may also be cheaper to pay further in advance than at check in; I can't remember (but the OP could look it up at jetstar.com as well as I can, so u won't bother).