The ALP could well win control of both Houses if a double dissolution occurred soon enough. A double dissolution means exactly that, a full Senate election, not the normal half-Senate.
It is for that reason I don't think he will do it unless he is convinced he will win both Houses. He might hand the Greens more Senate seats that they would otherwise win- or even allow the Democrats to win a seat in SA. Keeping the minor parties in check is a bigger issue than winning government to major backers of both majors.

I am on record saying we will have such an election, I believe it
It would be the only chance Labor has of controlling both house for ten years, things move slow in the senate.
Such an election would remove family first, forever, the senator from SA may survive but Labor would be unlikely to win control of both houses.
It would be easy to dissolve both house and a wise move, much of Australia is not impressed with independents in that house watch this space we have time yet to see it happen.