As the public eagerly waits for good news, the Royal Children's Hospital is not expected to release any information about the progress of the operation until 4pm on Friday, with Dr Crameri to give his first update on the girls early on Saturday morning.
Nima and Dawa underwent surgery on Friday.
Head of paediatric surgery Dr Joe Crameri, who led the operation, said there had been no surprises despite fears the girls' bowel were shared.
"We saw two young girls who were very ready for their surgery, who were able to cope very well with the surgery and are now in our recovery doing very well", he told reporters.
Nima and Dawa Pelden were connected at the torso and shared a liver.
As well as the issues with mobility and comfort, Lodge said the twins had recently been losing weight, which had been a concern to doctors who are now observing them closely.
Since then, they have been staying at a property at Kilmore, north of Melbourne, which is run by Children First Foundation, which funded their flights and procedure.
Elizabeth Lodge, from the charity, said Ms Zangmo had felt "a little bit scared", but had shown "extraordinary calmness" before the procedure.
She will spend Friday praying and meditating. "She tends to. always be on the top, pulling rank, as we say, and Dawa's more placid", she said. Luckily, Dr Crameri said, humans are born with more bowel than we need, making a separation possible.
"She still has this extraordinary calmness about her, which is just incredible".
One of the biggest operating theatres has been commandeered for the procedure, which will involve two teams of anaesthetists - one for each sister.
Several members of the surgical team had worked on the operation to separate conjoined Bangladeshi twins Trishna and Krishna in 2009.
About 18 people were in the operating theatre - including Bhutanase paediatric surgeon Karma Sherub, who flew into Melbourne this week. They could stand but only at the same time.
"We saw two young girls very ready for surgery, were able to cope very well with the surgery and now in recovery doing very well, " he said.
The girls, who were joined from the lower chest to just above the pelvis, arrived in Australia with their mother Bhumchu Zangmo about a month ago.