Upgrading to iPhone 11 Pro Max from iPhone 8 Plus w/o visiting the Apple Store
I did same, moving from iPhone 6 to 11. All I needed to do was take out SIM card and put in new device. SIM card was same size.  I recommend you purchase the 'sim-free' or unlocked phone from Apple. It costs the same, and does not lock you into a carrier. It also supports AT&amp;T towers (as well as verizon etc). If you purchase the AT&amp;T phone, they generally want you to change your plan, update it or hassle you to death :)

There is no need to contact AT&amp;T, as they do not require registration or activation as does say Verizon. I don't know if this is technical or just policy, but no need to call or configure anything, just put in the SIM Card. 

Be sure to backup your old phone to either iCloud or to iTunes on your Mac/PC. If you use iCloud, simply sign into iCloud on new phone, and iCloud will load all your apps and preferences from the old phone. If you use iTunes, simply attach your new phone to your PC/Mac and restore your data to the new phone.  If  you are using iTunes for backup, be sure backup using a password/encryption. If you do not, any passwords or logins will not transfer.