Here are the drivng time estimates.

If we get away from Canberra by 11am on the 1st we could drive pretty
easily ( plenty of rest stops ) arriving in Nygan or even Cobar by
nightfall on the dec 1st and reach Broken hill by early-mid-afternoon
December 2nd.

When going to watch the Leonids in SW QLD a few weeks ago, I left Canberra
at 1130am and reached Nygan by 6pm, Bourke by 930pm.  At nightyou have to
drive NYG_BOURKE slowly due to Kangaroos.

               DIST(km)        DRIVING TIME (from previouslocation)
Sydney to       -              -
Canberra        300            3-4 hrs
NYGAN          550            7 hrs
Broken hill     600            8hrs
Tibooburra      340            4-5?  Road is pretty good most of the way
Ft Grey         100            2-3 hrs (allow extra just in case)

TOTALS          1890           24 hrs

               DIST(km)        DRIVING TIME (from previouslocation)
Sydney to       -              -
Canberra        300            3-4 hrs
NYGAN          550            7 hrs
Bourke          204            2 hrs
Tibooburra      400            7   Road is not too bad but worse than
Silver City HWY
Ft Grey         100            2-3 hrs (allow extra just in case)

TOTALS          1550           21 hrs