You absolutely can bring your own stroller into both the Disney theme parks and the water parks. With a three month old child, I would very much recommend that you do bring your own stroller rather than rent from Disney. The Disney strollers are not, in my opinion, padded or plush enough for such a young baby.
If you look at this page of travel tips for people with small children found
HERE, you will see a button on the right hand side of the page that says "Height Requirements." Clicking on this link will bring you to handy pdf that you can download. The pdf lists the attractions in all four theme parks and both water parks that have height requirements. If an attraction is not listed on this document it means that there is no height requirement and any age child can enjoy the ride.
The height requirements are also listed on all the maps at the parks and on signage in front of the various attractions.
Have a great vacation with your family!