Earlier this week, Apple released iOS 12, watchOS 5, and tvOS 12, so naturally, the next day was when we got the first betas for the upcoming "point one" updates. Today, the iOS 12.1 and tvOS 12.1 public betas are available, while there is no public beta offered for watchOS.
There is one big issue that you might be aware of though, and that's that there's no iOS 12.1 image available yet for the iPhone Xs or iPhone Xs Max, so if you're picking up one of the new devices when they come out tomorrow, you might not be able to install the beta. This is an issue because if you plan on restoring from an iCloud backup, you won't be able to restore one that was made on iOS 12.1 on an iOS 12 device. In short, if you're buying one of the new iPhones tomorrow, you might want to skip this one.
Of course, nothing is stopping Apple from releasing the images when the devices are released tomorrow, and they'll likely exist for beta 2.
The first iOS 12.1 beta brings back group FaceTime calling, a feature that was announced at WWDC and included in the iOS 12 betas, but was pulled shortly before launch. What's not included just yet are the new emojis that Apple promised would be delivered this year. Those will likely arrive in a later beta build.