Was wondering about the Flu shot for babies?

So my doctor today recommended that my 9 month old get a flu shot. She at first said the spiel like a brochure. So I stopped her and asked her what she personally thinks. She said she thought it was a good idea because my girl was a preemie so she has a weaker immune system and high risk of developing pneumonia from the flu. At that moment I thought okay sounds right so I got them to give it to her. Now I am having second thoughts. Has anyone else's baby had the flu shot? She gave me a thing to read but was wondering what others experiences with it was. I know I can't undo anything-lol but just looking for reurance. We have to go back in a month to give her the second plus the doctor wants us to get it so we don't p the flu on to my girl. Any thoughts or opinions, thanks