I do not think you need a second opinion at this time. A breast bud generally does not suggest that there are any significant hormonal problems or that this is related to breast cancer (if there is a family history of breast cancer, I would mention it to your child s doctor). By having her examined, the doctor gets a good history, checks to see if there are any other signs of puberty, any evidence of secondary sexual characteristics developing, or other possible causes for the lump.
Reassurance is appropriate along with just observation over time. If the area seems to be infected, seems to be getting larger, or discharge is noted from that nipple, then I would have her reevaluated.