Currently, only organs may be taken from those who have signed the donor register or if their next of kin have given permission.
But due to a shortage of donors and long transplant waiting lists, there has been an ongoing debate in the UK on changing the system.
There are 300 people are currently waiting on transplants in the region.
The Upper Bann MLA is introducing a Private Members Bill at Stormont for a move to the 'Opt out' scheme, which would mean everyone is presumed to have given consent to be an organ donor after death unless they state otherwise in writing.
Mrs Dobson's son received an organ transplant and is a long-term advocate of signing the organ donor register.
"Mark has received the precious gift of life, but sadly for some this gift comes too late, or not at all," she said.
"As a mother I fought hard for my son, but as a politician I will fight just as hard for everyone else, because everyone deserves the chance of a new life. However, the fact remains that people needlessly die every year while enduring the wait for a suitable organ to be found.
"A simple change in law can make a massive difference in practice, for patients and for their families.
"The change I am proposing will help to save lives. Moving from the present 'Opt in' to a new 'Opt out' system takes organ donation to the next level."
A family friend of the assembly member knows firsthand the consequences of donor shortages.
At just 38, Justin Weir from Donaghcloney, Co Down, endures the four-hour, three-times-a-week routine of undergoing dialysis after a genetic disorder meant he had to have both kidneys removed.
"Eleven of my family members have been affected by kidney disease and this leaves a cloud of doubt hanging over our younger family members," he said.
"Knowing that more organs would be available would help and go some way to alleviate our worries for their future."
Mr Weir is in favour of the proposed change in legislation.
"They always have the option of opting out," he told UTV.
"This is the beauty about it and I believe it's a win-win situation, if they really feel strongly about it it's just a matter of opting out and obviously for us waiting on organ donation this will greatly increase our chances."
"We are delighted to have someone like Jo-Anne who has personal experience of this issue and can empathise with what we as patients and families go through every single day."
Mrs Dobson added: "This issue is much bigger than party politics and I am reaching out to politicians from all political parties to join with me to give the gift of new life.
"To change the law to make life better for dialysis patients, for worried families and for the future."