I have been thinking about this problem for a while as well. I am considering making a travel enclosure which is slightly smaller and much lighter. The real problem is the cost of the materials. I really have not thought of an inexpensive way to make it happen, but if cost is not a concern you can definitely make it happen.
I would recommend using an 80/20 aluminum frame which will be stronger than a wood enclosure and extremely light. What you use for the walls would be your choice, but plexi or hardboard would work. The cool part of the 80/20 would be that you could simply slide the walls, ceiling and floor into the grooves, no nails/screws. You can check out a lot of different options at 8020.net, the quick frame looks like the cheapest option which would still work. The only tricky part would be how you make the door to the cage, which is where you would have to get creative. Best of luck.