You can't put your carry-on bags by your feet or in your lap...they will need to go into the overhead bin. When it is taxing, taking off, under 10,000 ft., rough weather and etc., you can't get up from your seat. So what are you going to do if your child needs something like a bottle, a blanket, a change of clothes and etc...having a crying, screaming and/or fussing baby for 10, 20 or more minutes?

It is my recommendation to deal with a professional travel agent that works at a brick & mortar travel agency that has experiences with parents traveling with young children. The small price that you will pay for a booking fee will be worth it.