I've had some limited success shooting Fantasmic!. It is hard for all of the reasons that Groucho said. In addition, much of the action is relatively small and distant, so metering can be a problem. If you subject is only a small portion of an otherwise dark photo, your camera will have a tendency to overexpose. This would be a good time for spot metering.
I was shooting at an equivalent focal length of 260mm most of the time. I shot much of the show at f/2.8 and an ISO of 1600. You can get away with less, but you'll need to be pickier about when you shoot. Try to time your shots for moments, however brief, when your subject "poses" or stops moving. I had to crop many of the shots rather substantially, even at 260mm.
My first recommendation is to get the sign in the daytime. It's an easy shot and can be used for scrapbooking, slideshows, or any other case where you want to introduce the subject.
Here's a shot of Mickey "posing" with some fireworks. It was at 1/800 of second but could easily have been shot at a slower speed.
I tried a few shots of the "water screens", but nothing came out very well. It might work better to go wider to capture more of the context.
This shot demonstrates a few more problems that you need to deal with. The shot is at 1/100s, f/2.8, ISO 1600, so it's pretty low light. That's even with a relatively bright light on the scene. The other problem is that the lighting is very uneven. The bad guy is brightly lit but much of the rest of the scene is dim. You have not choice but to either tolerate the difference, crop closer, or spend ages in photoshop.
The parade on the water is similar to shooting Spectromagic, only it's further away. This was a 1/80s and, aside from not being a particuarly good composition, can't hold up to be enlarged at all well.
Here's one at 1/320s. It's a much better shot of the characters, but it doesn't show as much context.
The witch is a good "poser" and the cauldrun photographs well. This is a 1/200 second shot, so the light was pretty low. She was also pretty distant, so this is substantially cropped. It's my personal favorite of my Fantasmic! shots.
This was a mere 1/20s shot (even at f/2.8 and ISO 1600), so it really didn't come out very sharp. It's saving grace is that the subject isn't very detailed and the eye beams are what catch your attention anyway. So even as relatively blurry shot, it still works OK.
I got this shot of my wife and son at 1/50. It's not the sharpest, but it was a good expression capture. I think I was using the illumination from the fire on the water for this shot. If you don't think your gear is up to really shooting the show well, you might try capturing more shots like this and some easier wide angle shots and then just borrowing specific show shots. After all, we're all shooting the same show. You're welcome to my shots and many people here will let you use theirs for personal use if you ask their permission.
Mickey with the sword is another good "posed" shot and one with plenty of light (1/500s). The shot suffers a bit from the heat waves coming off of the water, which was burning moments before. I've seen some shots where the effect is much more pronounced and adds an interesting twist to the picture.
The shots of the character boats aren't too hard because they are relatively close and well lit. I just couldn't come up with any interesting compositions.
The final shot I took is another Mickey "pose" shot. It's relatively dim though and very distant. I think this was significantly cropped.
If you want to see more shots or look at the EXIF on the originals, you can see them on my Smugmug site. The Fantasmic! shots start
here and continue for a couple of pages.
With all that said, I think that Fantasmic! is one of the very hardest things to shoot well at WDW. It's dark, distant, and full of motion. The context is hard to capture along with the detail. I'd love to get a shot of the auditorium just before the show starts. I'd also like more wide shots, but I was too lazy to swap lenses during the show. I think that shooting with a non-DSLR is going to be extremely challenging and that you shouldn't expect to have too many keepers. Still, it doesn't hurt to try and you might prove me very wrong. If not, just download some of mine and tell everyone that you took them. They'll never know and I won't care.