Yes. Of course. But the causes of
heart disease in young children are usually different from the causes of heart disease in adults.
For example, a good portion (but not all) of heart attacks in adults are related to lifestyle factors (diet, obesity,
smoking, etc.).
In children, a heart attack may be caused by a combination of things, such as a genetic blood
clotting disorder, a faulty heart valve leading to an increased risk of
blood clots, and/or spasms of the arteries. Surgery in a young infant can also increase the risk for strokes. So can certain medications and diseases.
Artery spasms are a relatively uncommon cause of heart attack, but they do happen. The exact cause is unknown, and anyone of any age or health status can be affected.
So to answer your question, anyone can have a heart attack or stroke, including a baby. That said, the causes are typically different in infants that adults.
The baby is question's illness may very well increase her risk of serious medical problems. It's important to make sure she is under the care of a specialist who can care for her properly should anything go wrong.