The familiar is a mythological concept. Witches, wizards and shamans were thought to have a spiritual bond with an animal. The magical human was able to store her soul in the animal's body temporarily. Cats, foxes and toads were common familiars, but they could be any beast, bird or reptile. You and your sister could identify your own familiars; the animal tattoos would represent your spiritual connection.
Drawings your sister did as a child could be the basis of a truly individualized sister tattoo. If the old drawings are too crude to make an appealing design, your tattoo artist and maybe your grown-up sister can work with you to come up with ways to express that little girl's vision in more graphically sophisticated ways.
Families in most European countries identified themselves with a crest or a coat of arms. If you're not descended from such a family and don't have a real family crest, you can work with a tattoo artist to design one, incorporating symbols that represent your family in general and your sister in particular. You and your sister may get matching family crest tattoos, or you could do slight variations, with your crest containing symbols that represent her, and vice-versa.