I never shot biathlon, but I was a varsity smallbore rifle position shooter in college-so take it for what it's worth...
At 8 years old, focus on safety and marksmanship fundamentals (sight picture, sling use, maybe one session with open sights, one with peeps, one with scope-to get her acquainted to those platforms-who knows, many options). Don't ski with a loaded rifle. Load at the shooting area. Keep the clay pigeons close, to reward the shooter with a break ( ie 10 yards or 50 ft ? ). Maybe post one paper target (like a 50 ft pistol target with 8" black rings) for a 5 shot group/score, so to give an idea of how the rifle is sighted in.
Focus on prone position (more hits = more fun) for about 75% of the shots. Mix in a little offhand, for comparison, and future training.
Maybe have a "shooting session" before and/or after the biathlon mix, to reinforce fundamentals (and have fun).
Don't wear her out with skiing. You want her to enjoy the activity. Try it yourself. Learning by example is both memorable, and fun for both of you. It's a lot different shooting with a calm heart rate, compared to a heart that is pounding.
Keep it simple, and make it fun. Remember, she is eight. That means you are dealing with a person with VERY short attention span. Keep the number of "training points" to a minimum-but be resolute in reinforcement, and be encouraging, supportive, and patient. You want her to come back, not swear off the activity based on unrealistic goals (or anger, not implying you would do this-just covering the bases).
While I can claim I've outshot US Olympic Gold Medal Rimfire shooters in smallbore rifle (which is a good memory for me), my most fun shooting was when I started to learn how to shoot by my Dad when I was about 10 years old. We'd walk out behind our cabin in the Catskill Mountains (NY State) during the winter, and put down a plastic table cloth and a blanket to lay on in the snow. We would then take turns shooting icicles that hung from the rock outcroppings (from frozen spring drips) with a Savage model 24 22/410 and single shot 22 bolt (Erma). It was fun seeing the reactive targets break with a hit-but it was grand just being with my Dad and shooting with him.
I hope your "junior biathlon" is as fun and memorable as my icicle shooting gallery time.
Maybe you can make some colored ice cubes as targets (food coloring, orange, red, green etc), and put a piece of string in each for hanging. Try hanging some charcoal briquettes with kite string from a branch/board. We do this at our winter shoots at my muzzle loading club. Fun. We sometimes use a "clay pigeon board." You used whatever size sheet of plywood you can find (2'x4', 4'x4') and put in two nails about 1-2 inches apart on a horizontal line (so that you can place a clay pigeon on the two nails. The nails are hammered in so that about 3/4" or so (not critical) of the nail is exposed. You can place these two nails every 8 inches or so in a horizontal line and make a very nice reactive target zone.
Maybe have this as the range, and then have her ski a loop of some distance (25 yards?) to come back to the target zone, and fire another 5 shots or so from prone (put down a blanket for her to lay on, no need to freeze the child).
There are plenty of links for biathlon on the internet for more formal info. I currently live in Maine, and they have a strong biathlon program in the northern part of the state. Here's the link. Drop them a line for specifics. Good luck.
http://www.mainewsc.org/teams_biathlon.html