"I explained to her that we were just trying to help people who were a bit down on their luck."
He said his daughter had "a funny little way about her - she looks off into the distance and processes things".
On Wednesday morning, Kauri found a letter next to the microwave penned by Peyton, addressed to John Key.
He said he saw the words 'Dear John Key' and thought, 'what's this?'
It read: "My name is Peyton and I'm going to be the Prime Minister one day," Peyton Kauri wrote. "But right now can you please make the people that have to live in a car have a house. Thanks."
Her father said: "I read it and I was pretty blown away, this was coming from a kid and you don't really expect them to react like that."
Kauri said it was a proud moment for him, and a reminder that children were always watching parents' behaviour.
"Even though they might not say it, they're always taking it in."
"For a child of her age, being aware of problems in society and problems that are around us, that not necessarily everyone around us acknowledges, for her to see it and want to do something about it, yeah, (it) makes me a proud dad."
When Kauri asked Peyton when she wrote the letter, she responded casually that she'd written it "the other day".
Kauri said he was speechless. "I thought, 'This kid's onto it'."
Peyton had previously mentioned to her dad her plans to become Prime Minister, or as she had called it, "the big boss of New Zealand".
Kauri said he'd encouraged her jokingly, and told her she could do it if she wanted to.
Minister for Social Housing Paula Bennett thanked Peyton for her "thoughtful" letter.
"I think it's so cool that you have shown an interest in helping other people. The Prime Minister is overseas at important meetings so he has asked me to write back to you."
Bennett said the government was working hard to help the homeless, and it was a job she took seriously.
"We are building thousands of new houses, mostly in Auckland where they're needed the most...I hate knowing that some people don't have a place to call home which is why I'm always looking at ways we can provide even more help."
The Minister said she hoped Peyton was working hard at school and being good at home.
"I have absolutely no doubt that you could be Prime Minister one day and I wish you all the best."