Hi there, I know this was posted a few weeks ago, but you may still need advice. I've worked for years in a frame shop, and was pretty darn good at my job, so maybe I can offer some ideas.
If you take it to a frame shop, you can ask for them to put spacers between the glass and the matting if you'd like to just have it framed. They have clear and black sticky spacers that they'll put on the inside of the rabbit (the lip on the front of the frame that holds the glass and picture in place) once the glass is in place that will keep the glass from pressing against the metal. They look like this: http://www.lumierephoto.com/mm5/graphics/00000001/40-509_1.jpg
You could also cut a thin strip of foam core (use the 1/8", as most rabbits are 1/4" thick, and you don't want to see it peeking out from behind the glass) and use double sided adhesive to stick it to the inside of the frame. You could then paint the foam core to match the frame or mat.
Another option is to shadow box, and there are a lot of pre-made shadow boxes available that will save you a whole bunch of money, and are really simple to assemble. Custom ordering a shadow box is very expensive. When you mount things inside, you can either have a mat cut for the inside with windows for your photographs (like you would in a regular frame) with space left to top mount the license plate, or you can top mount all of it with adhesive on a solid piece of mat board. I would use glue lines on the back of the license plate, since it holds really well, and gives things a bit of lift.
Then there's also the option of taking an old frame, and building a box to fit around it to turn it into a shadow box. I've done this too, and it's very time consuming, but can be cost effective and beautiful.
Hope that's helpful, I'm happy to answer questions in more detail if you have any!