Do you collect/earn Qantas Frequent Flyer points when you fly Jetstar interstate?
You can earn qantas points on any jetstar fare including intrastate and international. But not on the cheapest base fare, you need to select starter plus bundle which comes at a fee.
On top of what Mark said, check out this page for more details if you haven’t already.
http://www.jetstar.com/au/en/flights/frequent-flyer-partners/qantas-frequent-flyer