Police were investigating whether Easton was left in the car while Ms Millar played bingo or the pokies at the hotel.
They allege Ms Millar left her son in the car, in 38-degree heat, for an extended period of time.
Lawyer Cameron Allen said the child was showing signs of recovery, but the timing of his recovery remained uncertain.
On Thursday, Magistrate Suzanne Cameron changed Ms Millar’s bail conditions, allowing her to visit her son.
Ms Millar’s mother was in court to support her daughter.
Mr Allen asked the court to suppress the name of Ms Millar’s mother, arguing that the grandmother had experienced “undue stress and embarrassment” since her daughter’s alleged crimes were made public.
But Ms Cameron rejected the application, saying there was often regrettable embarrassment caused to the families of those facing possible criminal charges.
“The Open Courts Act starts with a presumption of open courts, of transparency and the openness of justice,” Ms Cameron said.
Ms Millar is due to return to court on April 16.