That looks like a great carrier, Theresa
. Whenever I've flown w/ the kiddos, no one has ever measured anything, nor have they ever asked for a health certificate. The one you have is similar to the one I use for Wylie (he is bigger). For Marcel, I've used a Celltei, which I love - so nice and well made!
I don't think the one you have will collapse at all...there is usually some wiggle room w/ the measurements they give you.
Also, a tip for flying during summer...I find it can get pretty warm under those seats since the A/C never reaches down there. In the past, I've put frozen gel packs under the carrier's interior pad (or, under their blanket) to add a bit of coolness. Other things to put under there are those freezable seed packs or whatever they're called.
Have fun on your vacay, girly poo!