It's been a long time since I pulled my kids in a trailer--they're both in college now--but we all still have some great memories of those days. My two cents worth: Kids are only good for a limited amount of miles. After that, they just get bored and miserable, and then they make you miserable. You don't want to turn them against the idea of bicycles at an early age.
Also, as far as the risk goes, it's one thing to take the risk for yourself, it's totally another thing to expose your kids to that same risk. You're an adult, and you know what you're getting into. They're just trusting little creatures, and have no idea what you're getting them into. It's just not the same thing.
I have a better suggestion: Pack your bike, your trailer, and your little one and head on down to the L.A. Beach Bike Path. There aren't any hills down there, but there are a lot of headwinds, and your trailer will catch them all. There are lots of cool places to stop, not to mention the beach itself. Take a heavier bike, e.g. a MTB, and you'll work even harder.
One final suggestion: Get one of those trail-a-bikes when your daughter gets to be about four or five years old. They are just phenomenal, and the kids really love them. We had one with two seats that we towed behind our tandem, making it into a quad. It was really something!