In Machine learning, Datasets are used to find result as accuracy and predictions. So, If dataset behavior of past 10 years of baby symptoms of various sign, symbols and behavior is given. can we find diseases of baby?
"If the dataset contains past 10 years of baby symptoms of various sign, symbols and behavior", as you mentioned, then you can predict/classify the disease of the baby? But to perform this, your dataset need to be labeled. That mean for a supervised classification task each of the instances in dataset should be labeled with a corresponding disease name.
If you need further help, then I can help you. I have dome several disease classification researches.