Poj7:
Don't believe they take reservations, etc. At least they never did all the times we palyed.
We've had the best results at the very hottest time of the day--just like in real golf, when nobody feels much like playing!!
Sometimes at Fantasia, we'll arrive about 15 minutes before it opens. We're often the first (tho not always) on the course, and that certainly makes for a better, more relaxed game.
Been several times when we drove over to play and saw long lines--just went elsewhere.
BTW--tho not Disney, there is a miniature golf course at Pirates Cove, in the WDW Hotel Plaza area. It's an option if the Disney spots are full, or if you're looking for something different--.