There are some good answers here and some that don't address what you are looking to do. As previously stated, a "typical" escrow can be a couple weeks for cash and 30-45 for one involving financing. But, closing dates are negotiated between buyer and seller. Today's market conditions will make it difficult to schedule an extended escrow. Inventory levels are in the seller's market category. If a seller receives more than one offer they will take the one that will net them the most and can close quicker in most cases.
You should read your lease carefully and discuss you intentions with the landlord. There may be some flexibility, but you won't know unless you properly research and discuss it. If this is a house, the landlord might be willing to let you go early if a new tenant is found that can occupy sooner. It also sounds like you are planning on purchasing on your own, without representation. The key question I have is why? Do you feel you can get a better deal this way? I refer to the market conditions again and point out that many properties are getting multiple offers. In case you weren't aware of it, the seller pays all commissions in a transaction (unless specifically negotiated otherwise), yet you get the benefit of an agent working for you and not the seller. This includes locating and researching properties and handling documentation and the process for you. If you can get these benefits without it costing you anything, isn't it worth it? If you would like more information, please feel free to contact me. Either way, best of luck to you.