Bless your heart. I can sense from your beautiful heartfelt letter that you are really concerned about this issue. It is truly a blessing for the dear child whose mother desires to understand the unique challenges that children face. You are a woman who has a heart for children and in this you are able to see the challenge from a child view.
Many children grow up in homes where they are the only child. It is interesting to me that when my own children needed companionship they usually gravitated towards those children who were only children. In fact our eldest daughter married an only child. I believe that being the only child in a family can be a wonderful blessing especially if you are homeschooling. It would be a wonderful teaching experience to seek to tool your homeschooling day around activities that would be of interest to your daughter. For example, it is not healthy for your daughter to spend large amounts of time on her own but instead she could be learning from you different skills that owing to her situation you would have the time to teach. The two of you could find those activities whereby you are learning together. I take a yoga class on Monday mornings and in our class is a homeschooling mom who brings her 8 year old daughter. She is very respectful and works through the exercises to the degree that she is able. When the mom leaves she tells me that the two of them usually go to the grocery together. She is teaching her young daughter to cook. I think that since the Lord has given you this one child it is a further blessing for you that she is a girl. There is so much that the two of you can share together.
Certainly you need the companionship and fellowship of other homeschooling moms as well as your daughter. However do not be discouraged and do not dismay. The Lord knows your situation and He is ready to comfort you in this challenge. Rest in His embrace and bring your sorrows to Him. Jesus in His mercy hears your longings and He will provide guidance.
It is great that you take her to dance class. Perhaps depending upon the size of your town you could investigate the 4H. 4H is a wonderful organization whose membership is not based upon school affiliation. In this she will meet many children her own age. If there is not an active homeschool 4H group consider starting one. Merely ask for the guidance of those persons who are in charge of 4H in your group. It is very easy and straight forward. The 4H agents lead the meetings and do the teachings. Check it out and see what you think. Go to your local museums and see if there are times for participation through volunteer efforts. Though she is a little young it might be possible that the two of you can volunteer together on some activity.
Above all this believe in your heart that the dear sweet Jesus wants to help you with this challenges. Trust in His care.
Let us offer up our prayers this morning for all those families that are childless and are in the process of adoption. Let us pray that doors are opened for them and that they are able to continue in their efforts according to the will of the Father. Amen.
Sending out a prayer,