Most restaurants won't allow a stroller in a retaurant, regardless of the age of the child. Usually they only allow a stroller to be brought in if the child is sleeping. The highchairs at most WDW restaurants are the wooden kind, which are not suitable for a 3 month old. Crystal Palace and Chef Mickey's do have infant style highchairs so no need to worry there. When we traveled with our 4 month old, it definately was a challenge. He was too big to stay comfortable in his car seat, also it was August so too hot as well. He was in his regular stroller and we brought a portable bouncy seat with us. It folded up extremely compact, it fit in the bottom of the stroller. We'd set it up on the table next to one of the adults, and he'd stay there while he ate. Usually he wouldn't stay there the entire meal, so we'd end up holding him for some of it. If you're not going when it's going to be VERY hot, I'd recommend bringing the infant car seat. Also, these aren't the most comfortable for babies, so I wouldn't recommend planning on staying in the park all day with one.
Edited to add: I should clarify one thing. All counter service locations will allow a stroller to be brought in, it's just the full service, sit-down restaurants that won't allow a stroller.