I did one of my many trips to the UK when DS was two and a half and DD was sx months old, I found it hard but not too hard and I was by myself. DD had reflux and that was probably the hardest thing about it. Just make sure you get there early so you can have a seat with a bassinette then that will take care of the little one. I have always bought a seat for my kids (other then when she was 6 months old) because It's hard enough to fly with kids, let alone if they're on your lap. But saying that, you will have DH with you so that will be easier.

I, personally would get Izzy a seat but it all depends on finances.

From my experience you flying with a baby around 6/7 months is a perfect time. You can distract them with toys, they can sleep flat in a basinette and you can feed them when they're cranky! Older kids are harder but you'll know what Izzy likes to play with and there will be two of you to distract her. I was lucky that DS has always been a big movie watcher so he was happy to watch the tv for a lot of the flight, if not you could always buy a portable dvd player with and take some Wiggles movies or whatever she is in to.

Some great toys I have taken are little etch-a-sketch thingys, pens and activity books, felt activity scenes are great, packs of cards, books, puzzles. I usually take a carry on bag full of toys.

I have just come back from a trip to the UK with all three of them (7, 5 and 18 months) by myself so if you have any questions then fire away!

ETA - This last trip I gave DD2 something to make her sleep on the way back. A lot of people don't agree with this but it saved my sanity and the people around me so it might be something to look into.

Good luck, it's full on but lots of fun flying with kids!!