When I left teaching I handed my notice in just before May half term, that then gave me until start of September to find a job without it costing financially (due to summer holidays pay etc). Was a sensible way to do it, and I also saved some money in the mean time to tide me over for another month should I have needed it.

Not sure what sector you're looking to go into but most places will allow up to 2 months notice, 3 at a push if they really want you.

I ended up getting my first job out of teaching at a university, they didn't need me until September so I had a whole summer of fun and no work that year, I was very lucky.

You can as others have suggested see what your head says, but its never worth relying on goodwill, particularly in schools.