Have you tried shooting without the flash? Or learn to fix the problem in your image editing program.

Bill Silliker, who wrote the well-regarded book The Master Guide for Wildlife Photographers, took a lot of moose shots. If you try a site like Amazon you'll also find useful works like Joe McDonald's The New Complete Guide to Wildlife Photography.
A few thoughts: wildlife photographers often do need flash and face some challenges. One is that the way the camera deals with red-eye is to do some preliminary flashes so the eyes adjust. Pet photographers let their flashes off a few times for this reason. Obviously this is a problem in the wild.
There may be some very sophisticated software solutions but generally all Photoshop does is change to a credible color.
Flash light falls off pretty sharply over distance so you may need a pretty good flash unit or two. You can then mount off camera on a bracket.
Sounds like you're having fun. Personally I love moose, having run into them often in Northern Ontario.

Here are a couple of web postings on the topic, the first by a person who offers cautions about when to use flash with wildlife:
http://www.dmcphoto.com/Articles/Flash/index.html
and two that are more sanguine:
http://www.outbackphoto.com/the_bag/brad_fillflash/essay.html
http://www.naturephotographers.net/articles0903/jm0903-1.html