If your school has a PTA, I would definitely talk to them. It's possible that such a thing has been tried in the past, so they might have some good advice on how to go about starting a club.
You might also talk to your local library to see if they have rooms available for free or low-cost. That way you could start a club without going through the school and without it being in your living room.

How much time are you personally willing to put into creating and running a club? As a PTA board member, I hear suggestions all the time for after school programs we should offer. The people making the suggestions, however, aren't willing or don't have the time to run the programs themselves, though, so it doesn't happen. I'm not trying to put you off, but unless you're willing to put in most of the work (at least initially), you may have trouble getting traction with an otherwise fantastic idea.
As far as how much work and time is involved, I think it depends how much you want to get out of it. Scouting takes up a fair amount of time for the leaders and the (more involved) parents. The DIY club we belong to takes relatively little time for everyone (but we're pretty relaxed about it).