According to Official Guinness Records,
The fastest half marathon pushing a pram (male) is 1 hour 10 min 42 sec and was achieved by Matt Lemon (USA) at the Ohio River Road Runner's club Half Marathon in Xenia, Ohio, USA, on 9 April 2017. During the attempt Matt pushed his 20 month old daughter Maggie. Matt has been running in organised races since he was about 5 years old and ran competitively in high school and college.
For a complete list of 2017 records, please visit 2017 Guinness Records in United States.