You can usually still fly domestic without your passport if you have changed your ID or drivers license to a more compliant Real ID from your states DMV office.
If you don't have a Real ID or Real ID compliant drivers license then you'll likely need your Passport so if you have a passport it would be best to go ahead and bring the passport along with you to the airport when flying domestic.
However sometimes the TSA can confirm your identity through a database but to avoid any aggravation it would be best to have a passport along with you because it can vary depending on the airport and there policies.