Hi AndiE, i have travelled on my own with my two girls quite a bit. When i started DD2 was 11 months. A sling or carrier is a good idea, but they wont let you wear it for take off and landing, some weird airline policy. Anyway, i find the hostesses are lovely and always more than happy to help. I often ask them to either watch DD1 while i take DD2 for a nappy change, or hold DD2 while i duck into the loo. I go to the Loo at the airport where it is easier and i have only needed to use the plane toilet a couple of times. I find most people are happy to help.
One tip that someone else mentioned, carry as little as possible with you on the plane.