The petition seeks public support to vaccinate the five to 12 year olds.
Three doses of vaccines cost about $500 for those who are ineligible.
Andrewes' son Ethan is 11-years-old and daughter Larissa, 8, and said it was a pity she has to pay to get them immunised.
"Government should come to the party and think about those things because I think it's not fair that mums can get free vaccination for some of their children but pay for the others that don't qualify.
"Anyone can catch meningitis and with kids starting school next week, they'll be sharing taps and other things in school which will only increase the risk of infectious diseases," she said.
While out camping at Taupo Bay recently, Andrewes said they practiced safe hygiene as she was worried about the spread of diseases such as meningitis.
Dr Reti said many concerned parents were paying up to $140 to have their children vaccinated while others simply could not afford them.
"Meningitis doesn't ask their age. It is woeful that the government avoided expert advice that recommended that all others under 20 years of age should be vaccinated in this campaign, not just the limited age groups that were chosen," Dr Reti said.
"The government says the reason for the limited vaccination campaign is because there are are not enough vaccines but thousands have been sold through GP vaccine suppliers in Auckland. As a GP, I can buy dozens online right now."
Pharmac director of operations Lisa Williams said the eligible age groups were identified following clinical advice from its experts as well as the Ministry of Health.
She said under five-year olds were the group most affected once the disease spread, while 13 to 19-year olds were most likely to be carriers of meningococcal disease, but have no symptoms.
More than 25,000 doses of the two meningococcal vaccines, Menactra and Nimenrix, have been provided in Northland which was sufficient to cover 100 per cent of the age groups included in the programme, she said.
"There is limited supply of meningococcal vaccines globally, and our responsibility is to ensure there is enough stock to meet New Zealand's needs for the vaccine. This includes considering the potential need for stock in communities outside the Northland region."
To date, 11,396 of the 22,707 eligible children in both age groups in Northland have been vaccinated.