She can become a familiar but you don't exactly make her one. The first thing you would need to do is to bond with the animal and establish a friendship with it, that's most easily done by simply caring for it and spending time with it. That's basically ll you can do but you can also strengthen a magical connection by meditating with her and performing spiritual exercises with her nearby.
A familiar is an animal that you share a connection with and will lend you their energies during spell and spiritual work, it's a two way connection and very much a partnership between you and the animal.
I'm not sure where the idea that a pet is the same as a familiar came from. I guess I have to blame it on some of the crop of poorly researched books on the market these days. But the fact of the matter is that our beloved pets and a Witch's familiar are very, very different things.
A Witch's familiar is an animal spirit or a magical construct created by the Witch or the Magician as an adjunct to their magical workings, as a repository for power, and if needed as a defense against magical attack from another magic user. A Witch or a magician can draw upon the energies of the familiar when they need an extra boost of energy in a magical working. Conceivably if the spell is important enough, the Witch could completely drain the familiar of energy causing it to "die" or cease to exist. And in the case of a magical attack, the attack could be diverted to the familiar so that it would be the familiar which is destroyed rather than the magic user. None of these are things that I think any of us would want to do with our pets.
There is an excellent article on familars here: http://en.wikipedia.org/wiki/Familiar_spirit
Animals are very sensitive to the energies around them and they may be drawn to us when we are working magic because they can sense the energy. They also want to be around their people, which again will make them want to be where we are..and that may be where we are doing magic. Neither of these things makes the animal a familiar or inherently magical in and of itself.
Why can a familiar not also be a physical being? It is possible to have such a spiritual bond with physical beings as well as spiritual so I personally don't see a reason but I'm not an expert in the field which is why I ask. Certainly spiritual familiars are more useful and more common as they can be subdivided into many other names, animals spirit (or just plain spirit), servitor, thought form, etc. I shudder to think though that someone would be willing to work so closely with any such entities (except perhaps with the concept of self constructed entities such as servitor or thought form) and be willing to let them suffer by a magical attack in place of themselves.
The answer as to where the confusion of pet and familiar lies I think is probably to do with the merging of cultural beliefs. European familiars were for a long time seen as spirits that inhabited the body of an animal where as the native american system of free roaming animal spirits was a very separate idea. Through the improper understanding of the two being linked together it gave rise to spiritual animals (as opposed to animal spirits). That's a complete guess as to the origin but it seems a logical one to me as it's also something that can be quite easily popularized by the spread of fictional works.
