Lucas James Yarran, aged 20, and Leroy Smith, 19, were not required to plead to seven offences including murder, kidnapping and armed robbery.
Ms Fairhead was pushed out of a car at the entrance of the Joondalup Health Campus just after 3:00am on Wednesday before the vehicle sped away.
She was rushed inside but pronounced dead a short time later.
The court heard the men stormed a home in the northern Perth suburb of Ridgewood in the early hours of Wednesday morning while armed with a machete and a baseball bat.
It is alleged they kidnapped Ms Fairhead and two other people in the home, before stealing jewellery, mobile phones, a wallet and methamphetamine.
It is alleged they killed Ms Fairhead a short time later before dumping her body outside the hospital.
Late today police appealed for a third person, Ross James Boag, to come forward and contact them.
Detective Sergeant Anthony Thompson said the 19-year-old frequents the Joondalup area and may be armed.
He said the crime perpetrated against Ms Fairhead was a “callous crime against the mother of three”.
Several family members were in the court earlier today to support Mr Yarran and shouted out to him as he left the courtroom.
“Love you brother, stay strong,” they yelled before being ordered to be quiet and leave the courtroom.
The two men were remanded in custody and will appear in court again later this month.