Peer's match was played without any of the protests that followed her last week in Auckland, New Zealand, where she advanced to the semifinals despite anti-Israeli demonstrations.
Acting on a noise complaint from tournament organizers, police made five arrests and about 20 demonstrators chanted and blew whistles outside the downtown Auckland tennis stadium during Peer's quarterfinal match last week.
In other matches, Sara Errani of Italy beat U.S. Open quarterfinalist Melanie Oudin of the United States 3-6, 6-3, 7-5, and Jelena Dokic, a quarterfinalist at last year's Australian Open, defeated Britain's Elena Baltacha 6-4, 6-2.
Dokic said she's in better shape now than the same period last year.
"The start of the year is always difficult. You always get a little bit sore after matches but it's OK," Dokic said. "I feel like I'm fitter this year and hitting the ball better. It's just a matter now of how I'm playing in the match situations."
Dokic will play Peer on Wednesday in the second round.
In other results Monday, fifth-seeded Carla Suarez Navarro of Spain beat Yaroslava Shvedova of Kazakhstan 6-1, 6-2, seventh-seeded Zheng Jie of China defeated Kaia Kanepi of Estonia 4-6, 6-3, 7-6 (4), and eighth-seeded Gisela Dulko of Argentina beat Melinda Czink of Hungary 6-4, 6-2.