Hello Craig,
We took our grandson over a few times last year and he is coming with us tomorrow.
I don't know the rules are about checking it in with your luggage, but at the check in desk we are given one of these sticky luggage labels (the ones that they usually attach to your suitcase) to attach to the buggy which is not weighed. We keep the buggy with us as 2hrs until departure can be a long wait and it helps keep him out of mischief (
!) it's also handy if he's wanting a snooze.
We then hand the buggy over to one of the flight crew just as we board the aircraft.
Hope this helps,
Eileenx