If you have a questionnaire already from the LA, sounds like the school have contacted them.
Be aware that although yiy should be sure and make some response to the LA, you don't technically have to fill in the questionnaire.
What you could do is fill in name, age and last schools attended-and write N/A all over the rest of it.
If you do that though, you should add something like a letter and enclose it with the questionnaire, quote the the Perry Case in which Lord Slade said:
"Prima facie this opportunity will appropriately be given (as was done in the present case) if the Authority, having first allowed the parents a sufficient time to set in motion their arrangements for home education,"
(R v Gwent County Council Court of Appeal (Civil Division) 10 July 1985 JUDGEMENT BY-1: SLADE LJ)
and say that you will be taking some time to settle into your home based education and will get back to them by ......(you insert date, you could reasonably say Easter) and tell them more about the home based education you are providing.
That's pretty much what we did.
It's ridiculous, it really is, to expect you to give any details about the education you will be providing-as you have only just started and don't know how it will go yet.
Giving yourself that time, will allow you all to settle and to also decide how you will be providing the information (the choice is always the parents). Some people will choose to have a home visit, some people will meet with the LA somewhere neutral such as the library, some will get their home based education endorsed by a third person-and some like us, never have a home visit.
In eight years the LA have never met our children and have never seen any of their work (The children didn't want them to)
Instead the local LA declare themselves satisfied with the 'Educational Philosophy' and written report that we send in instead.
Have a look at the Elective Home Education :Guidelines for LA's (assuming you are in England-are you??) These were published by the DCFS-that spells out what the LA should be doing.
Have a look also at the bumpf on the excellent HE-UK site(I think the 'articles page is especially well worth a read-it's where I found the quote about the above case law) and also the new Education Otherwise site
Having read all of that you should have all the info you could possibly need to keep the LAs and EWOs at bay!