and your DD really still fits at almost 11 months?

Practice w/o the base at home, it's actually pretty easy -- if your DD doesn't usually wake while being transferred I doubt this will wake her.

We took the base once but DS had his own seat, so it was easy to stow the base under the seat in front of his (while DS sat in the car seat). In the airport we managed to balance the car seat, locked into the base, in our umbrella stroller (we do not own a Snap n' Go type of thing) while carrying DS in an Ergo.
I am too paranoid to check a car seat.

Ok, can I just say - we had one base and two cars-installing without base with kid in the bucket seat was the easiest thing in the world. Leave the base at home.

We just checked the base with our luggage with a sticker on it with our name, we didn't put it in any special bag and it came back fine. That would be much easier than lugging the base to the gate.

I also would figure out if you are better at installing the base or just seat-belting in the carseat without the base (it took my husband and 1 other person to get the base installed, I know I couldn't do it myself). If someone is picking you up at the airport, I would see if you can ship them a base from diapers.com (about $50) and have them install it in the car before they get you.