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Venod Skantha was arrested and charged with murdering Rush on February 4, 2018. At the time he was working as a junior house doctor at Dunedin Hospital.
His practising certificate was withdrawn by the Medical Council 24 days after his arrest.
It took the jury three hours of deliberations to return unanimous guilty verdicts in the November murder trial and for four charges of threatening to kill related to his attempt to cover up the crime.
The Medical Council confirmed this week the professional conduct committee investigation into Skantha's misconduct was ongoing.
A council spokesperson said the council aimed to complete professional conduct committee investigations within six-to-eight months.
Following the investigation, the council has the ability to review the competence or fitness of the individual to practise medicine or to bring a charge against them before the Health Practitioners Disciplinary Tribunal.
Skantha stabbed Rush to death in her bed in February 2018.
The High Court heard Skantha's motive for killing her was to save his job at Dunedin Hospital.
She told him she was serious about going to the police and his employer with claims he was "touching up" minors without consent, supplying them alcohol and offering money for sex.
On February 2, 2018, the pair shared a terse back-and-forth via a messenger service on social media with Rush ending the exchange with: "You know what you were doing when you did it. For that, you deserve everything you're gonna get".
Half an hour later she was dead.
The court heard how Skantha was already on thin ice at work after showing up in July 2017 while off-duty and after drinking, and treating a patient.
He only saved his job on that occasion by lying about his mother's death.
Skantha will be sentenced in March.