Reinhardt Bosch, 33, and Noemi Kondacs, 22, appeared via video link in Brisbane Magistrates Court on Friday after they were charged with one count each of murder and torture.
Mark Platt from Sun and Co Lawyers represented the co-accused during their brief mentions and said alternative representation is being sought for Kondacs.
Bosch and Kondacs only spoke when asked if they could hear the judge.
Bosch faces an additional charge of assault occasioning bodily harm.
The Magistrates Court does not have jurisdiction to hear bail applications for murder charges, and their matters were adjourned for December 5.
Queensland Police Commissioner Katarina Carroll on Friday said the pair were the baby's parents.
"Getting a brief from my officers, it was just the most horrendous and confronting scene that you could ever face as a police officer," Ms Carroll told ABC radio on Friday.
Ambulance officers called police to a home on Mount Samson Road in Yugar, north of Brisbane, about 6.45am on Thursday in relation to the unresponsive boy.
The couple were taken into custody at the scene where the infant was located deceased, police said.
"The investigations uncovered injuries to the child that are enough for us to charge with murder," Detective Inspector David Jackman said on Thursday.
Bosch made the initial call to paramedics, Det Insp Jackman said.
The couple were not previously known to police, and nor was the address.
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