Tony Aitken, 33, formerly of Melton Mowbray, lost control of his truck on 4 May and his son Luke was thrown from the vehicle.
The boy was celebrating his 12th birthday when he died at Langar Industrial Unit, in Nottinghamshire, police said.
He died later from injuries sustained when the truck fell on top of him.
The truck had three children in the front seat, despite the vehicle only being meant to hold two passengers, Nottingham Crown Court heard.
The other children in the vehicle, aged 12 and five, were treated in hospital for minor injuries.
Aitken pleaded guilty to driving whilst unfit and causing death by dangerous driving and was jailed for five-and-a-half years, Nottinghamshire Police said. He was also disqualified from driving for seven years.

There are concerns about the number of deaths at the hospital, which is at the centre of a long dispute over the future of children's heart services.
The medical director of the NHS, Bruce Keogh, said it was "a highly responsible precautionary step".
But some people have questioned the decision and its timing, 24 hours after a High Court ruling kept surgery there.
Leeds General Infirmary had been earmarked for closure by the NHS review to concentrate children's heart surgery in fewer bigger centres.
But that decision was quashed by a High Court judge on Wednesday.
Stuart Andrew, Conservative MP for Pudsey, who has led a cross-party campaign to keep the unit open, said it was a "very odd" decision coming after the jubilation that greeted the court ruling.
"We have always asked them 'is it safe at Leeds?' and the answer always came back 'yes it is'.
"What is the information that says that has changed?"
Congenital heart defects explained
He added he had not received one complaint about care.
Children who would have been treated in Leeds will be sent to other hospitals around England.
Affected families are being contacted directly by the trust and the review is expected to take three weeks.
Anne Keatley-Clarke, chief executive of the Children's Heart Federation, an umbrella group for different voluntary organisations, said she had raised concerns about surgery outcomes two years ago, and more recently parents had reported difficulties in getting referrals at Leeds to other heart units.
In a statement on the federation website, she said: "My concern is that it appears that managers and clinicians in  Leeds, together with the parent support group, have put their own interests ahead of the well-being of critically ill children and their very vulnerable parents."
Sir Bruce and senior managers from the Care Quality Commission visited the hospital on Thursday to say it must stop all children's heart surgery there immediately.
In a statement, Sir Bruce said: "The trust has taken a highly responsible precautionary step.
"Some questions have been raised by the trust's own mortality data and by other information.
"It is important to understand that while this information raises questions, it does not give us answers."
The chief executive of Leeds Teaching Hospitals NHS Trust said outside experts would be drafted in to help review "all aspects" of care.
In a statement, Maggie Boyle apologised to parents and families affected but assured them the trust always put the safety of patients first.
The CQC said it supported the trust's decision and it was in close contact with the trust to ensure effective arrangements were in place to protect the safety and welfare of patients.
Sharon Cheng, from Save Our Surgery - the group which is co-ordinating the fight to keep children's heart surgery in Leeds - said: "We're mystified.
"We don't know of anything that could justify this step."
Previously, an NHS review said surgery should stop at hospitals in Leeds, Leicester and London to focus care at fewer, larger sites, where medical expertise can be concentrated.
More than 600,000 people signed a petition opposing the closure plans. Many people were unhappy that children from Leeds faced journeys of up to 150 miles for care.
The leader of Leeds City Council, Councillor Keith Wakefield, said he was "shocked at the timing of today's events".

The four from Bangor's Cor Glanaethwy were freed by the fire service at 11:45 BST, half an hour before rehearsals were due to start at Wembley.
Musical director Cefin Roberts said they had been "sending us selfies from the lift to say they're ok".
"It's quite a drama at the moment."
Mr Roberts told BBC Radio Wales: "They've entertained the rest of the people stuck with them in the lift."
A tipper truck driver has been jailed after the lorry he was driving rolled, killing his son.
[NEXT_CONCEPT]
Children's congenital heart surgery at Leeds General Infirmary has been suspended as a review is carried out.
[NEXT_CONCEPT]
Four members of a north Wales choir spent two hours stuck in a lift at their London hotel, disrupting their preparation for the first live semi-final of Britain's Got Talent.