K.P.
First thought... preschool isn't about curriculum. Preschool is about learning to negotiate the social world and to start developing readiness behaviors and skills (what behaviors would your child need to have learned to be a good student).
Second thought... "subjects" don't really start until second grade and in some places beyond that. Literacy and number concepts are the primary focus of K-2 curriculum. NYS DOE website has curriculum goals for science and social studies, but these are taught using discussion, literature and hands-on activities.
Third thought... your child is three and will be four!! Is there something about public education that concerns you? If not, I would suggest trying a traditional preschool program and seeing how your daughter responds before eliminating school as an option.
Keep in mind that many of the activities you would be doing with your child as part of a homeschool curriculum at the preschool level are things that you should be doing already! Reading to her; taking her places so that she has experiences to draw from; cooking with her; drawing; writing letters; talking about colors, shapes and community. Does this need to be formalized into a school format?
I am not an advocate of homeschooling for many reasons, however when it is done well it can be a positive experience for the children. I used to babysit for a family who elected to homeschool their children. Their family room was converted to a school room (complete with desks, bookshelves and a chalk board. Mom had a set schedule for the children each day and EVERY activity was educational. For example, before going to the grocery store, the children would make the list, estimate the cost, figure out "who got what" depending on the location in the store and then were responsible for "paying". This task was differentiated for the children's ages and encompassed math (estimation/$$/time), language arts (spelling), and critical thinking (categorizing). This mother also enrolled her children in various community activities to encourage socialization and for their PE requirement. She homeschooled her children until 3rd grade and then had them attend parochial school. That mom recognized that her strength was in primary curriculum, but that content area would be too much for her.