Some LAs are very quick off the mark indeed and may get in touch as soon as they discover that you plan to HE, even if you haven't yet begun!
Which country do you live in? If you are in England, you may find this document useful: www.gov.uk/government/uploads/system/uploads/attachment_data/file/288135/guidelines_for_las_on_elective_home_educationsecondrevisev2_0.pdf Though it's ten years old, it is the most recent government guidance to LAs about how they should be conducting themselves. It's useful to be familiar with it and to quote from it if your LA steps out of line.
The need for deschooling is widely recognised in home ed circles, but may not be understood by the LA. Many LAs use staff who have no training whatsoever in home education and usually come from a school background. However, a settling-in period is generally accepted by LAs (see 3.11 of the above document), so I would describe it that way. If they press you to supply information immediately, tell them you are still formulating your approach and ask them to contact you in six months. As for your question of whether deschooling is legal, deschooling is simply the short-term use of a widely-accepted educational approach known as "autonomous education" in the UK or "unschooling" in the US so yes, it should be fine. However, your LA may not be familiar with this idea. If you are still doing it some months down the line (which is fine if it works for you), you may need to be prepared to educate the LA a bit about it and discuss how it works for your child. Feel free to ask here if you need any help with that. Some home educators such as me use the approach for many years and would be happy to help you think it through.
You don't need to accept a visit from the LA, and doing so is risky. Some people have positive experiences and others don't, even within the same LA, even with the same person. Agreeing to a home visit invites the LA staff, who may be poorly trained or simply not understand the needs of your child or your family, to make subjective judgements. If your child has had a hard time at school, having someone come into their home, which should be a safe place, can be threatening. The visitor may say things which will unsettle your child, such as mentioning the possibility of a return to school or criticising your approach. A safer way forward is to send in a written report describing the education you are providing, once you have had some time to get established.
In your report, give examples of what you have done and are doing, but ensure that any mention of future plans is well hedged round with phrases such as "we may", "we are considering", "my child has found an online course which may be suitable", etc. The reason for this is that case law has defined a suitable education very vaguely, but describes it as "achieving what it sets out to achieve". Therefore, ironically, giving detailed plans is worse than giving no plans, because if you don't achieve your plans then you could be said to be failing!
Good luck and I hope you enjoy it! Don't worry too much about the LA. The law gives parents great latitude to educate their children in whatever way works best for them.