PEGI Rating: Suitable for 16 years and over. Not for sale to persons under age 16.
Source: https://pegi.info/de/search-pegi?q=final+fantasy+xiv

You can encounter some really mean and inconsiderate people in this game and it can be really tough to deal with, especially when you are still new to the game and everyone is nitpicking you.

A number of experiences I went through while going through the MSQ hurt me for weeks or were so demoralising that it was difficult to see a way to continue playing.

Unfortunately, you encounter it sometimes and since adults can find it difficult enough to deal with, it's probably not going to be handled well by a 13-year-old. The fact remains that your daughter is playing a game not suitable for her age.

She needs to either take a deep breath and use it to grow (since a similar experience will likely happen in an online game in the future), or try the game again when she is older and better able to cope with such people.