I remembered this thread and just thought it might be worth highlighting that one of the women cyclists in the road race at the Olympics has a silver medal from the 5000m Long Track speed skating from the Winter Games.
Obviously if you're sporty with good quads there's little difference which sport you do as long as it requires strong quad muscles. I've heard previously about a rower switching to velodrome cycling, but this is the first time I heard of a speed skater switching over.
I'm guessing there are obviously similiarities in the muscle strength required by the two sports, although there's probably a few other bits needed to make a good figure skater.
I know a lady who's a number one ranked cyclist both in track cycling and road racing in her age class (she's about 40) and she actually was speed skating at my rink for awhile. Her coach told her to stop because she's so competitive at stuff that she'd have a high chance of injury, and because she's pretty much got more power than technique. She's a 130lb or so lady, and can deadlift and squat 300lbs. She was reasonably fast skating, too, the only 2 other speed skaters at my rink are (relatively) old men, but she'd easily keep up with them after only a month or so of total time on the ice ever.
I can't really see cycling as being bad as long as you do stretching to make sure things don't lose flexibility from it. Me personally, I do powerlifting and Olympic style weightlifting to help with skating, the only problem I find is the added bodyweight, that comes mostly from eating a lot anyway. Other than diet issues (which I could resolve if I had more money) it's pretty good crosstraining. Cycling I'm trying to get back into for cardio, as I don't skate as much anymore, that and skating, since I have much better edge control and try to practice things (ie, I'll stay in one spot and do 3 turns for 5 minutes) it doesn't burn as many calories as it used to. One thing I do like about cycling is it keeps the knees feeling good, mainly because it just gets lots of blood flowing to the legs, to flush out stuff, but also more blood flowing somewhere, more healing that can take place.
As far as speed skating, I've tried it once, and it's definitely fun, but it's not the same as figure skating. It's very apples to oranges. The shallow grind on them, you step on the ice and you'd travel like 2 feet in figure skates, you travel like 5+ in speed skates, just because of how shallow ground and fast the blades are. In some ways, speed skating is more fun, but figure skating has the artistic and emotional aspect that speed skating doesn't have. Most figure skaters I've heard of do transition quite well, but yeah. So if your daughter doesn't wanna switch, that's probably the reason why.
EDIT:
One difference too, between speed and figure skating is, speed skating emphasizes much more the quad strength, whereas figure skating emphasizes the glutes and hamstrings more, mainly due to the posture. Speed skating you hunch forward, figure skating you're trying to keep good posture through everything you do, and then jumps, while the quads are important, jumps involve mostly the hams and glutes. As for core strength differences needed between the two sports, no idea. But there's a difference, speed skating you can have huge hypertrophied quads and it'll help a lot, whereas figure skating doesn't really use the quads as much.