The good news is that bicycling is so easy, even a 13 year old can do it safely! (The better news is that, by teaching your daughter to bicycle safely now, she'll be a safer driver in a couple years when she gets a learning permit.)
I agree strongly with John re: problems tend to happen in towns and cities. I started my girls when they were 13 and 10. For the first month or so, our rides must have looked like "Make Way for Ducklings" on wheels; I led, the girls in the middle, and my wife at the back. We made sure everyone was on the right side of the road, not swerving all over the place, stopped for stop signs, checked both ways, etc. When we were sure they could survive in suburbia, we graduated to longer rides; a book store and ice cream store were both about 5 miles away, which was a good distance for newby cyclists to catch our breath before heading back home. If you can do something similar, starting April or maybe March, you and your daughter will be ready to go when summer comes.
Just a couple recommendations. For Mom, pick up a copy of John Franklin's "Cyclecraft." and read it. Make sure you get the American translation from British. You could also try John Forester's "Effective Cycling", but Forester needs editing to cut out the politics and autobiography before it would be as good a resource as "Cyclecraft" on riding a bicycle safely.
I've been impressed by a few web sites:http://commuteorlando.com/wordpress/on-the-road/http://www.bikexprt.com/streetsmarts/
And for your review and study:http://johnforester.com/BTEO/ECIL.pdf