its a very very very long flight. Are you thinking basic losmen or posh hotels? And you do know travel is by taxi's (some buses) with no child seats right? To be honest I thik you are mad! I loved Bali but wouldn't take toddlers there. And they wouldn't remeber it anyhow.
I agree with Riven, it's a very, very long flight. Mind you, we intend to go next year when DS1 is 2.5 and DS2 will be about 6/7 months BUT that's only because we will already be visiting family in Singapore and that would just be a short flight away from there.
Avoid Kuta Beach like mad, it's awful. If you are looking at hotels, look at hotels in Jimbaran Bay where it's a lot quieter, the beaches are private and lovely. If you do rent a car, bear in mind they are all slightly mad drivers there. And car seat safety is practically non-existence in most of the SE Asian countries. I would also consider renting a villa rather than stay in a hotel with two such young toddlers. Having said all that, the Balinese are the nicest people ever and love children so you will have a great time when you do get there.
Would you consider the Maldives instead? Only 10 hours flight, very similar climate and beautiful beaches! We went there recently with 18-month-old DS and we all loved it like mad!
I took DD to Bali, Lombok and the Gillis the week after she turned one. I did it on my own (loan parent), and would reccommend it. I had been before though so knew what to expect.
I love Kuta, it's mad but great fun, though we were in Lombok when the bomb exploded so it wasn't much fun coming back. We went to the memorial service.
Travel isn't too bad if you keep the distances fairly short or get an air con taxi. No car seats though so be prepared for that
I'd stay in somewhere like Nusa Dua, in a nice hotel where you'll have a private beach, and then do some trips out of there. Ubud is well worth it for a few days if you can. Loads to do there and fabulous food.
I'd go back in a heartbeat. Great island and fantastic people. So child friendly.