Can i homeschool my 5 year old daughter who has selective mutism and is showing some signs of improvement?

My 5 year old daughter has had selective mutism ever since she was 2.5. Just recently,she has started saying thank you to few children and also throws ball to them in park. That, in itself, is a huge acheivement if you really know selective mutism. After the improvement in the park, i took her to library story time where she stood stonefaced with anxiety. So, i am wondering whether i should send her to 7 hour long elementary school. Please let me know whet you think. All your suggestions are helpful.