My OPT expires on January 29th, do I still have time to apply for an H1B?

My OPT is going to expire in January 29th and my emoployer is willing to sponsor me. What are my options? Do I still have time? Can i apply for H1B after expiration date? I know i wont be able to work after expiration date but can i work after i apply for H1B before it is approved or denied?

Thank you for help.