No, it won't happen automatically since 18.1 hasn't been released yet.
Assuming the 18.1 beta is available for the new phone, you'll need to set it up as new, enroll the device in the beta, install 18.1, erase all content and settings, and then finally do the setup/transfer process.
Another option would be to have the 18.1 beta IPSW file downloaded ahead of time. Be sure to get the right one for the new phone. Then put the phone in DFU mode and install the beta (don't bother setting it up first). After it's installed, go through the setup/transfer process.