9, 2 and 2

The only way that the product could be 36 and still leave two possibilities is when the sum equals 13. These possibilities being 9, 2 and 2 and 6, 6 and 1.

When friend said "I can tell you that the oldest daughter, who is at least a year older than the other two" this rules out the possibility of 6,6,1.

So the daughters ages are 9, 2 and 2.