K.,
I know it's hard to understand how the doctor can make a diagnosis like that without your daughter being able to tell him anything. But trust me, they can. Farsightedness has to do with the shape of the eyeball itself and where the light hits the back of the retina. That is something that the doc. can see just by looking in her eye. My nephew is about 9 mos, and wears glasses. They say that the prescription for a child that small isn't and doesn't have to be exact. Where an adult can say which prescription looks clearer, a child can't. But it does not hurt the child's eyes. It's very important that her eyes are trained to focus the light properly. As for the lenses being very thick, they will be if she has astigmatism. I don't know a whole lot about astigmatism, but my mom, sister, and best friend have it. My sister and friend have great vision (neither farsighted or nearsighted) besides the astigmatism and their glasses are pretty thick. I'm not sure why, but very small children seem to have very thick glasses too. My nephew's are unbelievably thick. But it has to do with training the muscles that hold the eye straight and training the ones that are in the eye to function correctly so that they focus right.
I know it can be intimidating to ask a doctor questions sometimes. But don't be afraid to do it. You are the only one that can voice concerns about your daughter's well-being. If you don't understand how a doc. came to a conclusion or doubt how true it is, ask. Ask him/her how she can tell that she needs glasses or how the glasses are going to help or why their so thick. Your doctor is there to diagnose and treat problems, but they're also there to help you understand they body and what it's doing and why.