Been travelling with my kids since they were a month old. Feeding items including water and hot water is permissible, Just put all the baby needs in one bag so they can inspect only that bag.

Stroller is another thing. Some airlines will pick up from you at the aircraft door or departure lounge and return when you leave the aircraft. Some will just send it through with your luggage and you pick up at the carousel which is a pain.

Been lucky that my kids don't seem to be troubled by changes in air pressure or turbulence. They only make noise when they're hungry.