Pre-approvals may only be good for a given period of time, depending on your lender. As long as nothing changes, it's no trouble to update your pre-approval if you need longer to find your home.
Your post is tagged for "Mufreesboro, TN". In this area inventory is currently low. So, I would schedule your lender interviews now. Once you have your credit/lending situation in order, then start interviewing agents.
Depending on your price range, type of financing, size/type of home, etc., you could close in 3-6 weeks. For your peace of mind and lifestyle, I'd start looking in February or early March. It's possible you could get under contract before your lease is up and have to pay an extra month's rent, so prepare for that. Bidding is competitive and inventory is low, but not putting an extra timeline contingency into the offer is an easy way to make it more attractive. Your Realtor should be able to help you through this one step at a time.