The majority of magicians don't seem to have much interest in making their own props, which is why you can't find detailed plans of the type you're seeking. The Magic Nook is more or less devoted to "Do-It-Yourself" magic, and you can get individual e-book articles on a variety of props and routines very reasonably, along with e-mail help to back it up if you should run into problems.
We currently don't have a bunny box or a mirror box article, because it is also a "Wizard style" magic site, and Wizards don't like using boxes and tubes and mirrors when just a tap of the old wand will suffice.
However: In the book "Tear-able Magic," by Eleazar Goodenough, he has an article about tearing up tissue paper to make a three dimensional top hat, which can then be used to produce a small rabbit.
The WAH Production Box in the Wizards' Journal #10 can be adapted for a rabbit production (it currently suggests a stack of fishbowls as the final production load). WAH stands for Westgate/Aldini/Histed whose principles have been combined in the box. Jim Gerrish added the final touch, but refuses to call it "WAHG" because that sounds too much like coughing up a hairball.
If you're not in a rush, I happen to know that Fred Goode and Jim Gerrish are collaborating on "Peter Cottentail" for the NEXT issue of The Wizards' Journal (#11) which will be out some time in October. That involves an invisible rabbit that becomes a visible live bunny at the end of the routine and has lots of Easter eggs bouncing around to add excitement. They are building the prototype now and it will be photographed for the article.
I hope that helps somewhat.