It may be tagged, but you will have to pick them up and drop off at JQ. They will check if you(UA) have paid for (23kg?) baggage as part of the ticket when you check in. And likely put a JQ tag on it. UA cannot check you into the JQ flight
From your JQ link
Jetstar will transfer your baggage between:
Connecting international Jetstar flights and flights with our partner airlines, where both international flights were purchased on the same booking
You are not connecting from an international JQ flight
You are putting too much faith & trust with UA
Here is Australia we know how they operate.
When are the flights?
After your trip please report back on how it went.