I'd start by checking your local hardware store. Pet shops often have this kind of stuff to but they might stock sealant rather than adhesive/glue, so a hardware store is a better bet*.
Maybe there is something even better for gluing rubber, you should ask the staff for advice.
You definitely need something that has plenty of elasticity, possibly something waterproof? (Is she played with in water or just for display?)
*you can still find non-toxic (aquarium and food safe) brand in hardware stores, but you have to read all the labels to be sure. Stuff that is made for aquariums is always supposed to be non-toxic when used properly