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In April, when PEOPLE reported on the pregnancy, Williams, 25, had been spotted attending prenatal yoga classes in Australia.
Ledger, 26, who most recently appeared in The Brothers Grimm and the skateboard movie Lords of Dogtown, split from actress Naomi Watts, a fellow Aussie, in April 2004.
Ledger and Williams costar with Jake Gyllenhaal in director Ang Lee's soon-to-be-released gay cowboy romance, Brokeback Mountain, for which Ledger received near-unanimous raves on the film-festival circuit.
As Gyllenhaal tells PEOPLE: "Heath wears his heart on his shoulder. (With) that kind of sensitivity and strength his child will feel safe."
JOSH & FERGIE: ROCKED BY SCANDAL
Did he cheat with a stripper?
Married less than a year, the couple denies an Atlanta woman’s claims that she and Josh had a fling
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