Dear T.,
At about 9 months a baby's brain has finished the work of developing so that he or she can recognize differences in people - for example, that is why they cry when they see new people. They suddenly know that is a stranger, and they don't know how to react. Just be calm, and love her and put her down again. Nutricious foods help that little darling brain, and a peaceful household with music and laughter and discipline will make her a secure and loving child.
Do not worry, and do not take her to a mental doctor. They are idiots sometimes. I took my husband to a mental doctor and it was a catastrophe and I had to pay $400 for that ! Yikes.
Really, I should not be telling you not to take her to a doctor, but I should be encouraging you to do some research on 9 month old babies on the internet. www.drgreene.com and About.com/pediatrics can help you a lot.
You are a good mom and you will know when to take her to a doctor - but first, read. O.K.?
Sincerely, C. N.