Hi Jason,
Don't worry no reservations are needed for Fantasmic at Disney's Hollywood Studios. The show is an elaborate mix of fireworks, lights, lasers and characters and is held in a huge amphitheatre which seats about 6,500 guests. It is incredibly popular though and I would recommend you arrive at the theatre at least 45 minutes before show time, even earlier at busy times.
To cut down on wait times there is a dining package that you can purchase, you can find details by clicking
HERE. You can dine at either Mama Melrose, Hollywood & Vine or the Hollywood Brown Derby, the meal is included on the Disney Dining Plan and reservations can be made up to 90 days in advance on 407-939-3463. This gives you access to a reserved section of the theatre, but seats are still on a first come first served basis.
Fantasmic can be quite dark and noisy in places and as your child is quite young I would definitely suggest you watch the show on a site such as YouTube so you can decide if your child would enjoy it!
Have a great trip,
Jo