Apple's Animoji feature - along with the Memoji update added in iOS 12 - is available only on the X-series iPhones: that means the X, XR, XS and XS Max. Which is to say that only those phones' front-facing cameras are capable of creating an Animoji recording - other devices can play them back and share them with others.
If you're willing to look further afield, however, it's possible to create animated emoji recordings on different iPhones and even non-iOS smartphones. These won't officially be Animoji, but depending on how shameless the third-party app developer has been in its imitation, they're likely to be a close approximation.
(Mind you, our experience suggests that because they do not have access to Apple's sophisticated facial-tracking sensor array they are not quite as accurate at copying the movements of your face.)
Let's look at a few Animoji alternatives.
This was an odd case. MrrMrr appeared to straight-up rip off Apple's collection of Animoji - panda, poop, cat and so on - yet not only was it approved to appear on the App Store, it was actually selected as app of the day at one point last autumn.
But the penny appears to have dropped since then, and nowadays MrrMrr has a far more limited selection of emoji filters. (The pug dog is quite good.) There are somewhat more realistic lion and koala faces available in the Masks section, and it appears in the app drawer in Messages, just like Animoji.
MSQRD doesn't copy Animoji directly, and its graphics are less cartoony, but offers a similar face-tracking effect.
Tap Catalog, then select Animals. There's a decent panda, tiger and jaguar (or possibly leopard), and the orangutan is fantastic.
Emoji Me Face Maker
This one's a little different. Rather than sophisticated face-tracking, it lets you create your own emoji, much like Apple's own Memoji (or Samsung's AR Emoji), which will be animated in pre-scripted ways. These custom animations are accessible via the app drawer in Messages.
It's free on the App Store.