The car was driven by a 17-year-old who can’t be named for legal reasons.
The teenage driver pleaded guilty to manslaughter and several other charges.
The now 19-year-old was sentenced to 10 years in prison, which is the maximum sentence for a child unless it can be shown the crime was particularly heinous.
However, Queensland’s attorney-general is now appealing the sentence on the grounds it is “manifestly inadequate”.
The family of Field and Leadbetter have been fighting to have the teen re-sentenced.
“The original sentencing we weren’t happy with and we thank everybody who has got us this far in getting this appeal,” Matthew’s father, Russell Field, said.
“And now we just got to wait for the judges to hand down their decision.
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“That could take a couple of days or weeks, who knows.”
The Department of Public Prosecutions claims the teenager falls into the cohort of repeat young offenders.
The state is trying to have the 10-year sentence increased to 14 years to reflect the seriousness of the crime.
The teen’s legal team is also in the process of lodging a legal appeal to reduce his sentence to nine years.
They claim the reduced sentence would mean he can be properly rehabilitated when he is released.
The court of appeal judges have reserved their decision until a later date.