The pair have been fundraising in recent months after being ordered to leave their religious retreat. The Examiner reported they had raised more than $127,000 in crowdfunding.
Mother Irene Gibson, of a group called the Carmelite Sisters of the Holy Face of Jesus, was ordered to vacate the compound at Corran South near the village of Leap in West Cork by next June.
That followed a 2019 conviction for breaching planning regulations in relation to the premises, which she set up as a religious retreat in 2016.
The Irish Times earlier reported Sister Anne Marie, formerly Hannah Loeman of Whanganui, professed her vows of obedience, chastity and poverty in May 2019 to become a Carmelite Nun of the Holy Face of Jesus.
"I arrived here from New Zealand in March 2017 and in September 2017, I received the habit as a novice and today I have made my first profession of vows for a period of three years," Sr Anne Marie, told The Irish Times in 2019.
"I chose the order because they are devoted to our Lady and reading about the life of St Teresa and praying and discerning the will of God."
Living in a wooden hut, she admitted that adjusting to a life of silence and contemplation was difficult at first.
"We are a silent order but one hour every day, we have recreation and can speak. We pray in common in Latin but when we pray in private, we have a choice of Latin or English but we only attend traditional Latin rite masses," she told the newspaper in 2019.
"After professing today's vows, I am obliged to remain for three years and at the end of that period of time if I am sure that it is not God's will, I am free to leave or to make final vows for life to live as a Carmelite nun."