From a Tiny Coach:
At our gym, we have a Tiny Exhibition team where kids can be as young as two years old. This team learns a short, slow routine and they compete in-town a couple times a season. Coaches kneel in the front and we have two or three helpers who go on floor with them to direct traffic and help with stunts. However, I know a lot of programs don't offer this, and she is too young to be on a competing team. If you do find and exhibition team there are some things you need to ask yourself about your child's readiness. Is my child potty trained? Is my child able to spend time without me? Would my child be upset or afraid by loud music or crowds? Most importantly: Can my child follow basic directions? This is very important. Cheerleading gyms are big places with lots of people tumbling, stunting and jumping. So when a coach tells a little one "You need to stay here" or " Don't go over there" they MUST listen and follow or else risk injury by getting tumbled or fallen on. (As a coach it is absolutely terrifying when a little one bolts into the path of a tumbler.)
In terms of an early start, cheerleading will help her with a lot of fine motor skills such as hand-eye, balance, jumping with two feet, not to mention social skills such as making friends, listening and following directions, teamwork, and taking turns. In terms of actual cheer skills, there are a limited number of things you can teach a two-year-old because of their limited muscle mass. A child her age can definitely learn a forward roll and a cartwheel. But there are things you can;t teach a child so little such as a backward roll, handstand, and back walkover simply because their little arms aren't strong enough to hold themselves up yet. The advantage comes in motions and stunts which she will definitely have a head start on.
I'm going to be blunt, yes cheerleading is dangerous. Any sport that requires acrobatics, tumbling, or lifting other people is inherently dangerous, and yes people do get hurt, sometimes die. But, the number that never have a serious injury greatly outweigh the number who do, and finding coaches who are committed to a safe facility and proper skill progression is key. Allstar cheerleading is typically more safe than rec because they are practicing on a spring floor (better than grass or a dead mat) and the coaches are more often accredited and first aid certified. At her age shes not going to be doing tucks or extensions, so other than a skinned knee or a bumped elbow, you're pretty safe. In terms of issues later in life, As far as I know there has never been a study that has tracked competitive cheerleaders to see how it effected them later in life. This sport is still very young and there is very little research. Is it possible? Definitely. But any more than any other sport? I don't know. Tumbling does beat your body up and fliers who stretch a lot are bending their backs in ways that are not normal. Like I said it is a possibility. I've never known it to mess with anyone's period (except for girls who were thin to begin with), though I suppose it might. These girls aren't training 7 days a week like elite gymnasts though.
In conclusion (sorry this post is so long winded) Look for a Tumble Tot class or an exhibition team at an Allstar gym. If you can find that, turn to a gymnastics facility for a year. I don't recommend a Rec league. Even if all she gets out of it is a good time and a chance to burn off some energy, there's nothing wrong with that. Any other skills are an added bonus. Best of luck on beginning your career as a cheer mom :)