We travelled to NZ with Natty at that age and she was brilliant. I realise your travel time is longer though so can understand your concern.
When travelling to melbs by myself with Phoebe I found the staff can be amazingly helpful when you're on your own with a bubba. I am sure they will be delighted to hold bubs while you duck into the loo. If you're not comfortable with that, you will manage bubs on your lap while having a wee, LOL!