The little ones emerged from their mothers' pouches a few weeks ago and can now be seen in their enclosure.
While the female joey was reluctant to venture out of mother Ruby's pouch at first, zookeepers say she is making up for lost time and exploring the outside world.
"She got off to a slightly slow start, but she's healthy now and starting to mouth leaves," koala keeper Laura Jones said.
"Ruby is also becoming more comfortable and relaxed as a mother and her joey can often be seen snuggling in her belly when they are resting."
Ten-month-old male joey Bardin is also out and about.
Named after an Aboriginal word for ironbark, he is the first joey for mother River, which is part of Taronga's breeding group.
The joeys are among the three bred successfully this season, following the three bred in 2013.
Baby koalas usually take up to eight months to grow in their mothers' pouches before they emerge.
The Duke and Duchess of Cambridge announced on Monday they are expecting their second child.
The royal couple visited Taronga Zoo in April with their son, Prince George, to unveil the bilby enclosure named after him.
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