How much did she eat?
Aloe is considered toxic to dogs. Common signs of toxicity are vomiting, depression, diarrhea, anorexia, tremors and change in urine color. The seriousness of the toxicity are related to the amount (dose) eaten.
You can call the Animal Poison Control Center ((888)(NNN) NNN-NNNN if you dog is showing clinical signs or you can get your vet to call if you plan to take her there. Either way, there is a charge, but if you are taking her to your vet, it might be best for your vet to get the info first hand.
If a dog eats a lot, the clinical signs can be severe. If they don't eat much, it isn't very dangerous. The seriousness is related to dose eaten. "The runs" or diarrhea is caused by toxic chemicals in the plant. In aloe it is a glycoside that irritated the intestinal tract. Aloe is sometimes used as a herbal purgative.
If she just broke it apart and is not having signs at this time, she should be OK. I would not suggest doing anything except monitoring for drooling and vomiting. They would be the first signs followed by diarrhea. If she starts to vomit, withhold all food and water for 6-12 hours and then offer small amounts of water for a few hours followed by small amounts of food. You most likely will not see these effects if she is not currently showing signs.