When I was in your position (leaving my first real job) I gave them 90 days notice (twice the time I estimated it would take them to find a suitable replacement

When I was in your position (leaving my first real job) I gave them 90 days notice (twice the time I estimated it would take them to find a suitable replacement for me); and I volunteered to do the technical screening of the new candidates and transition the workload over gradually. I ended up working side-by-side my replacement for the last month (training them); which was ideal for everybody. That ex-employer ended up being an invaluable professional reference, and we're still good friends. Protect yourself of course (maybe don't mention it until your plan B is solid) but treat them as you'd want to be treated...it'll pay off in the end.