There is a genetic part of the disease but exactly how much it not known. Studies show that children of a parent with the disease have an overall 5-10% chance of having it themselves (there is a 1% chance of having the disorder for those without any reletive with the disease). But there are also enviromental factors that they don't yet understand. In studies of identical twins about half the time that one twin has it the other twin won't. If it was only up to genetics then it would be 100% of the time.
The other thing to remember is that childhood schizophrenia is really quite rare. It does happen and you should be on alert for it but usually the disease presents itself in college aged people (18-24). You ask if this is something your family can handle. When you answer that question don't imagine a 3 year old or 5 year old with the disorder but an adult. In other words if you have other children in the home and are worrying about how you would handle them AND a child with schizophrenia it is most likely not a situation you will have. If she does develop the disease chances are that any older children will be out of the house or older teens who can help out around the house.
http://www.schizophrenia.com/ has a wealth of information on the topic. I presonally wouldn't turn it down just because of the diagnosis but I have worked in the mental health field so it isn't something that worries me. KWIM. I've known real people with it who end up leading good productive lives and so the diagnosis doesn't scare me the way it might someone else. At the same time you know your family and your situation better than anyone else and if, after reading more about it, you feel that it is not something you can handle then I would move on on hope that a family who is better able to meet her needs will come forward.