This character is a Other Symbol and is commonly used, that is, in no specific script.
The glyph is not a composition. Its East Asian Width is wide. In bidirectional text it acts as Other Neutral. When changing direction it is not mirrored. U+1F430 offers a line break opportunity at its position, except in some numeric contexts.
The CLDR project calls this character “rabbit face” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: bunny, face, pet, rabbit.
This character is designated as an emoji. It will be rendered as colorful emoji on conforming platforms. To reduce it to a monochrome character, you can combine it with Variation Selector-15: 🐰︎ See the Emojipedia for more details on this character’s emoji properties.
The Wikipedia has the following information about this codepoint:
Rabbits, also known as bunnies or bunny rabbits, are small mammals in the family Leporidae (which also includes the hares), which is in the order Lagomorpha (which also includes the pikas). Oryctolagus cuniculus is the European rabbit, including its descendants, the world's 305 breeds of domestic rabbit. Sylvilagus includes 13 wild rabbit species, among them the seven types of cottontail. The European rabbit, which has been introduced on every continent except Antarctica, is familiar throughout the world as a wild prey animal, a domesticated form of livestock and a pet. With its widespread effect on ecologies and cultures, in many areas of the world, the rabbit is a part of daily life – as food, clothing, a companion, and a source of artistic inspiration.
Although once considered rodents, lagomorphs like rabbits have been discovered to have diverged separately and earlier than their rodent cousins and have a number of traits rodents lack, including two extra incisors.