You're looking for an infant carrier which is Group 0+, not 1+, there is no such group as 1+.
I would first double check your own infant seat - if you look on the underside it should have an orange sticker which shows the maximum weight. Some infant carriers are still sold as Group 0, which only fits up to 9kg or 10kg but these tend to be very rare these days. It might be the case that it's truly a Group 0 if it's an older seat, a lie-flat seat or it came with a travel system.
Group 0+ is 0-13kg so should fit your 11 month old (unless they are enormous) regardless of being over 9 months. Generally you can ignore age ranges on car seats since the weight and/or height of the child is much more important, ages given are just a guide.
I agree that if yours isn't suitable, the Joie Juva would be a great budget buy. There isn't much point spending loads to get a top rated 0+ seat as it isn't likely to be suitable for much longer. If it's just this one trip that's what I'd go for, personally. Or see if somebody has an old Maxi Cosi or Graco or whatever knocking around which you can borrow.
Otherwise if your DC2 is over 9kg (which is likely) then you're looking for a Group 1 seat. Unfortunately none of these are particularly portable, although I did come across this the other day on another thread, which looked like a good compromise: urbankanga.com/
If you can't get hold of that one (the other posters seemed to find it difficult) then you could look at the Joie Elevate which is a Group 123 seat (highback booster with harness) which weighs about 5.5kg - I'd go for this over the slightly lighter super-budget ones (Often decorated with Frozen, Cars etc) simply because the fit will be a bit more reliable and those super-cheap seats don't do very well in safety testing whereas Joie does alright. However, it's a very grown up seat for an 11mo, you might not necessarily need the booster function, and so you might be more comfortable with the Joie Tilt which is also fairly lightweight (as they go) at 6kg, and would allow you to keep your baby rear facing (much safer until well over a year) with the option to fit forward facing if you really needed to or as s/he gets older.
You can get car seat bags which have rucksack type straps to transport these seats a bit more easily but they are a pain compared with booster seats and infant carriers.
If your baby is under 9kg then your only options are the Tilt or the Group 0+ seat because they can't yet go into a Group 1 seat.
Lastly another option might be to rent a car seat when you get where you're going, which would eliminate the airport question entirely. Car hire places usually rent car seats (although I have heard horror stories and they can be expensive) but you can also try googling Baby Equipment Hire + City and sometimes there are companies which will deliver a suitable seat to the airport for you.