Nineteen people, including 13 children, four employees and two firefighters died in the fire on May 28 last year.
They included New Zealand two-year-old triplets Lillie, Jackson and Willsher Weekes.
Their father, Martin Weekes, told APNZ evidence that the nursery was not licensed was a joke.
His children had nursery diplomas signed by the centre's co-owner Iman Al Kuwari.
Mr Weekes said he was baffled about why the issue of whether the centre was licensed was so important to the trial.
"The issue surely here is 13 children and six adults were killed. Whether the Al Kuwaris were in breach of their license operating as a nursery or a daycare seems to me to be irrelevant," he said.
"Why was a public building allowed to be built and continue operating when it was known to have illegal building materials? Why were there no working sprinklers and no alarms? Why was the water pump not working?
"Why were the children and staff not evacuated? These are the issues."
Al Kuwari's driver also gave evidence to the court, calling into question the timeliness of the emergency response, Doha News reported.
He said firefighters did not arrive until at least 11.10am, even though his employer had notified him of the fire at 10.20am. All other witnesses previously testified that the fire began around 11am.
The defence will continue their case later this month.
At least some of the defendants, including Al Kuwari and her husband and four mall officials were expected to give evidence.
The criminal hearing to determine responsibility for the deaths had been postponed four times after Al Kuwari failed to show up.