To begin, there is a difference between speech and language. Speech is the sounds we make. If she is pretty understandable when she talks than she probably doesn't have a speech problem. Language is the rules of language, like sentence structure, vocabulary, and social communication. It sounds like she has more of a language problem in communicating with her peers. It may be helpful to model the actual things she should say to other kids. Tell her, 'You could say...' and then fill in things like 'Let's play' or 'Hi friend' or 'That's cool'.
My advice: since she is three she is eligible for testing through your public school district. Call the school and arrange for a screening. From there they will determine if she needs further testing, based on educational standards. By the way, this is all free!! If she qualifies for therapy that will be free too.
More advice: do not call any attention to what you consider 'stuttering'. Things like 'take a breath' and 'slow down' do not help and may make it worse. The best thing to do is to give her uninterrupted time to say what she wants. It's hard but letting her talk while all others do nothing but listen is the best. There is a normal period of 'nonfluency' during the preschool years and this may be it for her. Allow the school professional to determine if it is stuttering or not.
R.