Scott and Donna Hussey's son, Freddie, suffered fatal head injuries when he was hit as he walked with his mother in Bedminster, Bristol, in January 2014.
Bristol South Labour MP Karin Smyth raised the case of the family in the Commons in a special debate.
A minister ruled out new legislation but has agreed to meet with the family.
Freddie Hussey was killed when a two-tonne trailer became detached from a Land Rover and careered across the pavement,  crushing him.
Andrew Jones, Parliamentary Under-Secretary of State at the Department for Transport, said new legislation could be "disproportionately burdensome".
Scott and Donna Hussey have been calling for a test similar to the MoT which would be applied to trailers and towed equipment.
Mr Jones said figures for 2014 showed there had been 1,257 road accidents involving towed vehicles, in which 39 fatalities and 214 serious injuries were involved.
But he said he would meet with Freddie's parents who have campaigned on the issue since their son's death.
After the debate Ms Smith said she was pleased the minister "took this issue very seriously" and that he had set out a number of clear actions that he has pledged to undertake.
Tony Davies, 37, from Hallen, was found guilty of causing Freddie's death through careless driving.
He was sentenced to 200 hours of community service.
The parents of a three-year-old boy killed by a runaway trailer said they were "disappointed" no change to the law is planned to improve their safety.