Its possible the baby could get it, you should look into them, some cancers are hereditary some are contracted. Keeping the child healthy and looking after them and talking to doctors will keep an update. The chances run about 5-%15 chance if i remember correctly. Cancer runs in my family heavily also.
I can relate to this concern as I also have an extensive family history of Cancer (on both my mother and my father's side). And, it's hard to say exactly what one's risks are on an individual basis... without benefit of genetic testing/counseling.
But, if you want to know the overall, general statistics, 5-15% of all cancers have a genetic predisposition.