I may leave my current employer for a new job. I want to be fair to my current boss. Should I give them early warning?

It is important to make sure your current employment remains secure until you receive an offer, accept the offer and receive a start date for your new job.

I understand you wanting to be fair to your current employer. I even commend you for it. You will be fair to them by giving proper notice when the time is right but it should not be at the expense of your current job. Wait until everything is all set with a new company (especially the start date) and then give proper notice (between two weeks and a month). You never know what could happen between now and then- you never receive an offer, the offer is not what you expected, the position falls through, you decide to stay where you are- so do not put yourself in an awkward (and potentially job threatening) position until the right time.

Well run companies are set up to deal with many potential eventualities- including employees leaving for better opportunities. They will understand you are moving on to a better job for you and appreciate being given enough time to hire a replacement.