Your physicians are completely correct. The timing of when to have this removed is up to you as a parent, and there is not a significant amount of medical guidance that can be given about the optimal timing of removal. Removing skin tags is a very benign procedure, and is usually done with curved scissors in your doctors office. Sometimes, your physician will place a small amount of material over the skin tag prior to cutting it off, just to help reduce bleeding. While there are other ways to remove these as well (such as freezing), often simple excision with surgical scissors is best.
The real crux of your question is whether or not you will harm your daughter by doing the procedure now, or if you would be better off waiting until later. Given your comment that the skin tag is near her eye, there could be some value in waiting until she is old enough to hold completely still. From the standpoint of scarring, usually the removal of a skin tag is so simple that there is very little, if any, scarring that is left after the procedure. There are other issues as well, such as the brief discomfort that she will feel, that must be considered. Consider to counsel with your pediatrician
or family practice doctor about optimal timing, and when he or she would feel most comfortable removing it. Alternatively, if you remain concerned since the tag is on her face, you could consider visiting a surgeon
trained in facial plastics (either a plastic surgeon
or otolaryngologist with facial plastics training) to completely optimize the outcome.