When I was in school I was placed in a gifted program that was housed in a separate building. I am also a fourth grade teacher, and in my district the gifted students aren't identified until third grade. Our model is a pull-out program. These programs aren't meant to be stressful to students. They are designed to enrich them beyond what they could do in a "regular" classroom. I'll be honest, it is very difficult for me to meet the needs of my six gifted students this year, and I am majorly in favor of the type of program your daughter's school has. I LOVED it as a child.
In addition to academic benefits, a gifted program has social benefits. Most parents don't realize that gifted kids may struggle socially. Although not all kids are this way, but many tend to be "quirky" and stand out socially. Peers have difficulty relating to them because they often have deep knowledge on many topics, process quickly, and may be considered weird (not saying anything about your daughter). By placing gifted children in a program with other gifted children, they are surrounded by students that may be able to "get" them. A downside, however, is that they may lose out on the opportunity to learn to work and coexist with students not on the same intellectual wavelength.
Whatever you decide, just know that as a parent you have the right to decline the services after she starts. If you feel it is too stressful, have her return to the regular education classroom. However, I have a feeling that once she starts you will feel very comfortable with her experience.