The only luggage lap children are allowed to "bring" is a gate checked item (stroller or car seat). So if you have two bags, toddler cannot bring a backpack.

Lap child = 1 paid seat that is being shared with an adult, right? Where would you fit it the item (during take off and landing when everything must be stowed safely) if you have your own personal item and carry-on bag?

You should check with your airline on their rules.

Does your lap child take a little toddler backpack with their toys, etc on the plane? Does this count towards the baggage total? I'd like to free up my personal bag from the toys for our 18 month old if possible.