Firstly, you made the right decision. Flying without a seat is a safety hazard both to the child and everyone around the child. Well done!
There is no LATCH on an airplane, if that helps. There really isn't any need to bring the base.
The reason you experienced 1 side flipping up when you tried a baseless install is that you were likely using a lap shoulder belt with a sensitive retractor (it kept 'clicking' back one more click and slowly pulling one side of the seat up).
Planes have lap belts only with a locking latch plate, so no retractor to 'click'. The seat can't tip at all.
It's actually incredibly easy to use an infant seat without a base, ( a lot less involved than using a base) you just need to get comfortable with it. Will you be in a car at your destination? Is there some sort of booster for your 5 year old?
Full Disclaimer, I'm not a car seat safety tech so this is completely just my opinion.
I flew with my daughter when she was about the same age as your daughter. I didn't (I know I should of from a safety standpoint, but it really wasn't in the budget) buy her a seat, but I did ask at the gate about extra seats so I was able to use her car seat (Graco Snugride 22) on two of the four flights. I gate checked her seat for the other two which made me a little less worried about it being checked. I'd say you're doing the right thing buying her a seat since I found the flights where she was in her seat were easier since she was used to riding in the car seat and it gave me a small break since I was traveling by myself. I'm not sure how the Keyfit relates to the Snugride, but I found installing the seat by itself with the lap belt to not be much harder than buckling myself in. The Snugride has notches on the top that you thread the belt through and across the top of the seat. If I remember right (DD is in a MyRide now, so her old seat is in our storage closet awaiting future babies) there's a level indicator on the seat itself so I was able to make sure it was at the right angle before I buckled her in. We used it that way in other people's cars a few times, and while I liked the fit better with the base, it did seem secure.
If I were you, I'd use the seat by itself on the plane. Assuming that the Keyfit attaches without the base the same as the Snugride, it's easier than it might appear and as Maedze pointed out you won't have to deal with any funky locking belts since airplane belts are about as basic as you can get. Since you're more comfortable using the base, I'd take the base with you as a carry-on. That would keep it safe from the baggage handlers, and then allow it to be installed in the vehicle you'll be using on your trip. I know the idea of taking it as a carry-on sounds a little weird, but it's no weirder than the Christmas my carry-on was the picnic hamper my aunt thought was a great present for people who were flying cross-country.
Hope this helps, and that you have a great time on your trip!
Married to my Airman since 12-23-06. Cloth diapering, baby wearing, breastfeeding AP mama to DD born 2/24/11
I wouldn't bring the base. It's just one more thing to hassle with. Also, I find that installs with bases tend to take up more front to back room, and front to back room is very limited on airplanes as it is.
For the car at your destination, I would install the seat and leave it in. Thats' what we did, just use it like you would a convertible. It's not as convenient as far as pop in and out, but way easier that continually installing.
C.- WOHM, CPST Instructor, and all around busy Mama to A.- 02/04, I. 01/07,E. 09/10 and
expecting the surprise of our lives Fall 2012!
Thanks for this thread, we will have to think about this issue when we fly with our 3 month old and 31 month old in November.
Happy , delayed/selective vaxxing, WOHM to DD1 4/10 , DD2 8/12 and partner/wife for thirteen years to SAHD DH.