Carvalho - who shares a house in Flat Bush, South Auckland, with her brother, sister and mother, who are all New Zealand residents - has appealed to the Immigration and Protection Tribunal, claiming the department hasn't followed its own policies.
It has underestimated her potential contribution to the country and says she has special circumstances.
"A lot of people see disability as an illness and it is not. I am not a burden," Carvalho told the Herald on Sunday.
"I have my wheelchair and ramps at my house that can be removed if I move and my family who support me here.
"I just want to have freedom of movement and the freedom to stay with my family. What is important is family, friends and being safe. I won't give up."
Carvalho has published an autobiography, In My Chair or Yours, which has been distributed to Brazilian schools as a learning tool.
She also launched a TV show in Brazil, Make a Difference, highlighting challenges faced by disadvantaged groups, and produced and directed the award-winning short film If the Eyes Cannot See, the Legs Cannot Feel.
She said it would be "heart-breaking" if she was forced to leave New Zealand.
Two of her siblings, including a sister who is a doctor, plan to move here at the end of this year.
"If I have to go back to Brazil I would have to live by myself again. I can live by myself but the point is that I want to build a life here and I should have the right."
Immigration New Zealand area manager Michael Carley said residency had been declined because Carvalho "did not have an acceptable standard of health to meet residence requirements".
He said the department "recognises" she had "emotional ties" to New Zealand, but these factors "were not considered sufficient to outweigh the significant costs and demands she is likely to place on New Zealand's health services in the future.
"In the case of Ms Carvalho, the likely costs for the lifetime of her condition were assessed as likely to be well in excess of $41,000 and therefore the threshold of imposing a significant cost was met," he said.
However, a review of her health by the Ministry of Health concluded: "All [costs] are dependent on Juliana's needs changing significantly due to physical deterioration which will possibly never occur."
A letter of support from Carvalho's doctor, Monique Huerta, added: "She is a completely independent person who does not need help with anything at the moment. I do not anticipate she will cost the Government any more money than a normal citizen in the foreseeable future."
