If its priced right, and inspections are done ahead of time, it can sell very quickly. If you started today, you could get most of the pre-sale stuff knocked out this week - cleaning, painting, repairs, de-cluttering, inspections, photos, etc.
Typically a good agent will want to have a open houses on two weekends and a Tuesday broker's tour. Pick a day to accept offers the following week. There may be counteroffers which may add a few days. Then, you go into contract. An all cash deal with no contingencies will close a lot more quickly than a financed deal. This is why, in many cases, the highest offer doesn't win.
Off course, you could get a pre-emptive offer that you decide to accept and close the deal in one day.
If you are worried about move out date, you can always make the part of the deal.