I didn't know R&M did a case for the Birdy, and had to hunt around a bit before finding it on their site. It's on page 35 of the folding brochure: http://www.en.r-m.de/fileadmin/medie...ten_2010_E.pdf

I see two problems with the case - it's too big to fly as normal luggage (201 cm = 79 linear inches), and it weighs about 19 lbs (8.6 kg) - even without the trailer kit - which eats up a lot of your weight allowance too. The nice thing, given the size, is that you need to do very minimal disassembly.

If you can stand to do a little more disassembly, I'd go with the Bike Friday case. It meets luggage limits and is much lighter. I borrowed the Bike Friday case from a friend of mine and the Birdy was an easy fit: all I needed to do was to remove the wheels and the stem/handlebars. Lots and lots of additional room for other luggage.