The company website says Ian White, the production manager, is also a volunteer firefighter at Lincoln.
Meredith White, the company accounts manager, also works part-time as a registered nurse at Christchurch Hospital.
The child received medical attention after being hit by the forklift but died at the family's rural property where the accident occurred.
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Family friend Alanah Tocker has set up a Givealittle page to support the family.
"A time of need has stuck one of our local families. Time for us to give a little and show our community support as this very tough time," Tocker wrote on the page.
"Jackson was a beautiful boy and treasured member of our community and will be so missed.
"This practical monetary support will help ease some of the everyday pressure on the White family to allow them to grieve."
Almost 60 people had donated $3849 to the cause by 10pm. The page says it will close on October 2 next year.
Two units from the Lincoln fire brigade responded to the call for help.
Fire and Emergency New Zealand area commander Dave Berry said their thoughts are with the family and everyone involved in this deeply sad event.
"We are providing support to the Lincoln Volunteer Fire Brigade including counselling and professional psychological support if required.
"Further support is also available to them and their families if they need it."
Selwyn District Council Mayor Sam Broughton said his condolences were with the family.
"It's a very hard situation for anyone to face."
Broughton said it was a very close-knit community and caring for each other was something they did well.
Police were first alerted to the incident on Robinsons Rd about 1.50pm yesterday.
They confirmed that a 4-year-old received medical attention but died at the scene.
WorkSafe has opened an investigation into what happened, but could not comment further.
A spokeswoman confirmed investigations can often take up to a year.