Emergency services were called to the village of Gratwich near Uttoxeter after the twin-engined plane crashed in a field.
Two passengers, including the child, managed free themselves, while three had to be cut from the wreckage.
Two woman were airlifted to Selly Oak Hospital in Birmingham, one with leg injuries and one with pelvic injuries. A man was airlifted to North Stafford Hospital suffering serious chest injuries.
Child hospitalised
A second man and the child were also taken by ambulance to Burton-upon-Trent Hospital. They were not thought to be seriously injured.
The aircraft is understood to have gone out of control above the crash site.
Staffordshire fire service said they received a call just after 1420BST.
Dairy farmer Mr Cotton was with his family at their home at Gratwich when they spotted the plane in trouble.
A spokesman for Staffordshire Police said: "They all saw the plane flying low over the farm.
Accident inquiry
"They said that it was making a strange noise and then they heard an almighty bang when it crashed in the ploughed field several hundred feet away."
Paul McCafferey, of Staffordshire Fire Service, saw the wreckage and believes the crash could have been worse.
"The plane was in a pretty recognisable state. There was some damage to the nose cone but other than that it was intact," he said.
The Air Accident Investigation Branch will launch an inquiry into the accident.