Disney service (they pick it up at your room) is out in the morning (before 8) and back by early evening and it ain't cheap. Can't remember actual prices but for a suit it is likely $12 to $15.
A possible different solution. Have it cleaned before going. If wrinkled because of travel: hang it up on hook inside bathroom door, turn on hot shower, close bathroom door, allow about 30 minutes and then remove. It will be a touch damp but will dry quickly and wrinkles will be gone.