Sorry stacychev- that must be so frustrating! Our GT teacher has indicated that this is a big problem she notices when she does her "push-in" units which frequently involve group projects.
In older grades, the organization of the project, as well as structure provided by the teacher, can help somewhat- in particular, when each kid has a separate, defined role I think things go more smoothly. That said, there are things which helped our kids manage.
Does your DD have any activities that are multi-age/ multi-grade? This was probably the biggest help in this area- our kids are in a martial arts program where they are grouped loosely by belt level but most of the class meets together- the higher belts are often tasked with teaching/guiding less skilled students. Great opportunity to see how everyone has different strengths, abilities, etc. We also talked often about which kids were good as teachers and why, how the goal is not to beat the other kid but to show them how to improve, etc. Everyone takes turns being a teacher and a learner- kind of a good lesson for life. (Love that quote that everyone you meet knows something you don't know...)
Also, just talking about different abilities has helped- it's easiest for kids to think about it in terms of how hard it must be for the classmate who is blind, or the friend in a wheelchair, but it can be extended to how hard it must be for the boy with autism or the girl with dyslexia, and the kid who just finds school harder than most. Not that any of the other kids she's working with have a disability, but pointing out that everyone has strengths and things they are working on. We used to say that so-and-so is still working on that skill, how can you help them, or show them?
Lastly, does your DD have any challenging activities/hobbies? We used these as talking points frequently- again, great for reinforcing that everyone has things they need to work hard at or struggle with. For some kids, school is harder- talk about how it would feel to be the kid for whom school is hard, ask your DD for thoughts on how she can help either the kid or the group to function more smoothly, etc.
Perhaps reassurance (from you or the teacher) that the project is not her sole responsibility would help, too- it's possible she is anxious that the work is not up to her standards, etc.
