He also faces charges of aggravated robbery and causing grievous bodily harm to Ms Aim, and intentional damage to property at a Taupo school.
He cannot be identified because of his age, and some details of his court hearing were suppressed.
The arrest would provide some closure for the family, as it would have been terrible to think his daughter's death could have gone unsolved, Mr Aim said.
He did not intend to come to New Zealand for any court hearings.
"Whatever it involves, I hope I can do whatever is necessary from this side of the world."
But the family intended to stick to a plan made with Karen to visit the country in March next year, only now it would likely be to attend an unveiling, rather than a family reunion.
"We intend to go out in March, and the mayor [of Taupo] is putting up some kind of memorial for Karen."
The visit would also give Ms Aim's family a chance to thank Taupo people who helped after the killing.
"So many people have done so much for us, we must come out and thank all these people in person," he said.
The youth's arrest came two months and one day after Ms Aim was murdered while walking home from a night out in the town, where she had been living and working for two months.
Taupo Mayor Rick Cooper praised police for their efforts, and said the suspect's age would be "a shock to anybody and everybody".
Christine Robb, who employed Ms Aim at her Lava Glass Blowing Studio, said the arrest was a relief.
"Everyone at the Lava Glass is still really saddened by the event but we're just happy that there's at least some closure."
Ms Robb hoped the news would also help Ms Aim's family.
"It will shock the whole of the Taupo community that it's someone so young."
In court, the accused entered no plea and was remanded in custody to a Youth Justice facility.
The boy stood with his hands clasped in front of him and was supported by a group of about 15 family members, some of whom waved to him as he was led away.
A great-uncle last night told the Herald he had been shocked to learn of the boy's arrest.
He had felt sickened hearing about Ms Aim's murder and like the rest of the community had wanted the killer caught.
"All I wanted to do was get him too, but when I found out who it was, oh jeez," he said.
The man said the accused came from a good family who had done their best with him.
View photos