The Text object supports the system default color emoji:
If you are trying to import a web font with different emoji, I'm not sure if that works... emoji normally have special separate handling in the browser/OS since they render with color, and I think sometimes there is the concept of font switching too - i.e. when finding an emoji character, it switches away from the current font to the system emoji font and renders the emoji there, so emoji always work in every font regardless of whether the font has its own emoji or not (and likely most don't have any). So support for emoji from a specific font probably needs to be specially implemented, and I'm not sure what the browser/OS support for that is like.