Cerys was 11 months old when the crash happened
Justice Secretary Jack Straw has proposed increasing the current two-year maximum jail term for dangerous driving to five years.
It follows a campaign for an increased tariff by the parents of a toddler who was paralysed by a car travelling at more than 70mph in a 30mph zone.
Driver Antonio Singh Boparan was jailed for 21 months. He served just six.
Cerys Edwards' parents welcomed the proposal. The change would not be enforced until after the election.
Gareth Edwards said: "We will always feel that Boparan got off lightly for what he did to Cerys.
"We hope that the change in law and the tougher sentencing will make people think twice about driving dangerously and prevent other people from being hurt."
He added: "It's taken 18 months but we finally got there. I always said I'd get this law changed and now we have. It's Cerys's law."
Mr Straw said reckless drivers who leave victims with serious injuries should get tougher punishments.
He said: "We have listened with great care to the innocent victims of dangerous drivers, their families and road safety groups and their experiences have directly informed these changes.
"However, introducing new laws takes time and so this cannot be put on the statute book immediately. This is inevitable when amendments to primary legislation are necessary, as in this case.
"It will therefore take some time before it can be brought into effect."
Cerys, of Sutton Coldfield, West Midlands, has needed round-the-clock care since the collision in 2006.
Boparan, the son of a multi-millionaire, was found guilty at Birmingham Crown Court in April last year.
The court heard he lost control while overtaking in his mother's high performance Range Rover.
The change in the law would bring into line the penalty for dangerous driving leading to injury, with those for drivers who cause death because their driving was careless.
In 2003, the maximum penalty for causing death by dangerous driving was increased from 10 to 14 years.
Road safety charity Brake welcomed the move but called on ministers to increase the maximum sentence.
Campaigns officer Ellen Booth said: "A charge of causing serious injury by dangerous driving, which should carry a much higher sentence than five years, is still urgently needed.
"We work with individuals whose lives have been devastated when dangerous drivers have left them seriously and permanently injured.
"Families who are left caring for their loved ones for a lifetime will still find it hard to believe they have received justice when a dangerous driver only receives a maximum of five years in jail.
"Dangerous driving is an extremely serious offence, often leaving victims brain-damaged, paralysed, and with loss of limb. We need to see the horror and severity of this reflected in sentencing."