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 night you have to
drive NYG_BOURKE slowly due to Kangaroos.

                DIST(km)        DRIVING TIME (from previous location)
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 previous location)
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