How to protect from the rabbits, find a cast off dog crate or one you can buy cheap. Take the tray out of the bottom and set it over the seedlings. Old dog crates work very well, even keeps squirrels out.
Milk crate would block too much light. It would be great for hardening off plants but not long term for plants that need full sun. Rabbits usually are most active early in the morning right around sunrise and then again right around sunset. If you have the time to move the crate every day it just might work.