Alexander Fitzgerald, 26, drove into 30-year-old Jasjot Singhota after not seeing her on a zebra crossing in Tulse Hill, south-east London.
He was driving a Ford Fiesta with frost on the windscreen when the accident happened on January 25, 2017. He stopped at the scene.
Dr Singhota, who worked for Guy's and St Thomas' NHS Foundation Trust, was taken to a south London hospital where she died the following day after suffering a traumatic brain injury.
The Metropolitan Police said she saved the lives of five other people through being an organ donor.
Fitzgerald was handed a 10-month prison sentence and a 23-month driving ban at Kingston Crown Court on Friday.
University student Fitzgerald, of Selwood Road, Essex, had previously pleaded guilty to causing death by careless driving and causing death by driving uninsured.
Dr Singhota's sister, Neha Santasalo, said the sentence "provides closure allowing us to focus on our sister, her life and all that she achieved".
She added that clearing a windscreen during cold weather is a "simple action that takes no time at all but can prevent any other family having to go through what we have".
Detective Constable Sejal Unadkat, who led the investigation, said the death of Dr Singhota "could have been avoided entirely".
Fitzgerald's 54-year-old father, Gary Fitzgerald, pleaded guilty to permitting the use of a motor vehicle with no insurance at Camberwell Green Magistrates' Court in May last year.
He was given eight penalty points on his licence, issued with a £250 fine and ordered to pay a victim surcharge and costs.
There were 164 casualties from crashes on Britain's roads in 2017 when a driver's visibility was impaired due to a frosted, dirty or scratched windscreen or visor, Department for Transport figures show.
One in eight respondents to an AA survey admitted they do not fully clear ice off their windscreen before setting off.
The organisation's president Edmund King urged drivers to ensure ice is removed from all windows and mirrors, adding that he often sees drivers "peering out of a small gap on the windscreen like a tank commander".
Neil Greig, director of policy and research at motoring campaign organisation IAM Roadsmart, said motorists need to "take every journey seriously and ensure they can see and be seen".