The Government has decided against banning rodeos because Associate Minister of Agriculture Meka Whaitiri did not believe they were harmful enough.
Rodeos operate under the Animal Welfare Act 1999 and relevant codes of welfare.
Jessie and Lyric said anti-rodeo sentiments did not faze them.
"Everyone has their own opinion. The focus for the team and the rodeo community is just to push past that and to do the best. We must ensure we're doing the right things and following the rules of rodeo."
The brothers said they blocked protesters out of their minds at rodeo championships they participated in throughout the North Island.
Abby Tauariki said she has urged her sons to ignore insults by anti-rodeo people on social media and not to engage with them.
For the Tauarikis, rodeo runs in their blood and they participate in the sport throughout the North Island.
Jessie and Lyric started rodeo when they were about five while their other brother who missed out on national selection, Damion, now 15, took up the sport at the age of 12.
The New Zealand Rodeo Cowboys Association selected 12 schoolboys— three for each event— from throughout the country for the Australia trip.
Mrs Tauariki received a call from the Association last week and she broke the news to the boys when they got home from Whangarei Boys High School.
"We're excited. They asked us to apply but we didn't think we'd get selected. There's real big competition from the Aussies who have got really good riders and ropers," Lyric said.
Training would be stepped up and the brothers' immediate priority is to get fit.
They have a makeshift gym at home and acres of farmland at Hukeranui to ride their horses.
Both compete in the second division rodeo and aim to participate in the open event, which is the highest level.
Jessie also plays rugby and Lyric does karate while Damion represents Horahora in junior rugby.
Dad Buster Tauariki said he was proud his sons got an opportunity to represent their country.
"It's a good start for them and it will only get better and better. They hope to get into the open event and ride the top bulls."