Haughey, runner-up behind Mollie O'Callaghan in the 100m at last year's event in Fukuoka, qualified third behind Australian Shayna Jack (53.50 seconds) and Fukuoka bronze medallist Marrit Steenbergen.
World record holder Sarah Sjostrom was entered in the 100m but did not swim. The Swedish veteran told home media earlier this month she is not planning to compete in the event at the Paris Olympics.
With world champion Tatjana Schoenmaker skipping Doha, American Kate Douglass is on track for a second title at the meet, topping qualifying for the 200m breaststroke semi-finals.
Douglass, who won the 200m individual medley this week, was runner-up to South African Schoenmaker in the 200m breaststroke last year.
Greece's Apostolos Siskos is top seed (1:56.64) for the men's 200m backstroke semi-finals in a modest field lacking holder Hubert Kos and former Olympic champion Ryan Murphy.
Finland's Olympic bronze medallist Matti Mattsson topped qualifying for the men's 200m breaststroke semi-finals with a time of 2:09.15.
Doha will be on world record alert in the evening session later on Thursday when China's Pan Zhanle swims in the 100m freestyle final.
The teenager set the world record of 46.80 seconds on Sunday with his lead-off swim in the relay and will be strong favourite to win his first individual world title in the event.
American Carson Foster will also bid for his first individual title as top seed for the men's 200 medley final.
