Hi Wendy!
Congratulations on your upcoming trip to Walt Disney World!
Fantasmic! is showing at Hollywood Studios on April 14th at 8:30pm. Realistically, you'd need to arrive at the park no later than 7:45pm to ensure seating for the show. You may find this to be a bit of a tight schedule for your first evening, but it is perhaps doable if you do have a park ticket you're willing to use for that evening's admittance. You'll want to consider making your dinner reservation a little earlier to be able to leave Downtown Disney by 6:45pm, taking a bus to a Disney Resort Hotel and then connecting to a Hollywood Studios bus.
For some 'nighttime magic' on your first evening without using a park ticket, I'd suggest that you take a bus from Downtown Disney straight to Disney's Polynesian Resort by 8:00pm. From the Polynesian's beach, you'll be able to catch both the Electric Water Pageant as it passes by at about 9:00pm and then the 'Wishes' Fireworks at 10:00pm. Afterwards, hop on the monorail to Magic Kingdom Park where you'll be able to board a bus back to Port Orleans Riverside.
If these times are too late for your little one, consider spending the evening at
Downtown Disney taking in the sights or even take a ride up the Characters In Flight Balloon for a spectacular, 360° view of Walt Disney World lit up under the night sky!
If you have additional questions about your upcoming vacation, please feel free to write me back any time Wendy! Wishing you a simply Magical time at Walt Disney World!
Kirsten