Okay, you have various options.
Your daughter only came out of school in June, right? So you could tell them that you are still settling into home education and helping your daughter recover from a difficult time at school, and you will send a report later on. By law you do have to be providing a suitable education from day one, but that doesn't entail doing formal lessons or having worked out a long-term plan. If you decide to do this, give them a date by which you will send in a report and then stick to it. A few more months should be reasonable.
Alternatively, if you want to get it over and done with, you could write a report now describing what your daughter has done and is doing, and what resources and social/educational opportunities are available to her. "Available" is the key word here. If she doesn't feel ready to take advantage of these opportunities yet, that is neither here nor there. You are PROVIDING suitable opportunities.
For example, on the social front: "She volunteers in a shop two hours per week, interacting with staff and customers. Has a close relationship with her mother, with whom she has frequent long discussions on a wide variety of subjects. Is very fond of her grandfather in Australia, whom she Skypes every week. Likes to play with her young cousins, and sees them about once a month. Engages confidently with library and supermarket staff and likes to chat with neighbours. Has previously enjoyed dance and swim classes, but no longer attends because the bullies from school are there. We are looking into alternatives and have identified several sports she could try in the autumn. There are also two dance classes in the next town which she can go to. Also, I have made contact with the local home education group and I understand there is a teen group which goes bowling regularly."
Notice that none of that promises anything specific for the future, but indicates that you have considered your daughter's needs and you are taking appropriate action in terms of offering her the chance to socialise if and when she feels up to it. You don't have to force her into situations she isn't ready for. You just need to indicate that you are leaving the door open for her to move out into the wider social world as she feels up to it. Socialising also doesn't have to involve organised group activities or be with people of her own age.
A third option is to refuse to provide anything to the LA, on the grounds that there is no legal basis for them to ask for it. Their legal duty is to intervene IF it appears that your child is not receiving a suitable education. You could ask them what information has come to their attention which makes it appear that your child's education is inadequate. ("What makes you think I am breaking the law?") If you take this course of action, there may be a few letters exchanged, which will either result in the LA backing down and leaving you alone, or in them threatening you with legal action. If they do that then you may well prefer to send them a report on your daughter's education rather than risk going to court - if you fight it you would almost certainly win, but it could be stressful.
Hope that helps a bit! Have a think about what you want to do. There are plenty of knowledgeable and helpful people on the HE forums who will be glad to advise. In particular, if you want to draw a line in the sand and refuse to provide information to the LA then you will want to ensure you know where you stand legally rather than just taking my word for it!