Your character's species: Sand domestic asian cat shifter thing
If your fursona/avatar was:

a general airborne species: Magpie
a general aquatic species: Uhh... sea serpent?
a general invertebrate: Moth.
an amphibian: Axolotl
a bird: Damn, mostly answered this one. Sparrow then.
a canine: Sheltie.
a caniform carnivore (excluding canines): Marten.
a dinosaur: Archaeopteryx.
a feliform carnivore (excluding felines): Aardwolf.
a feline: Sand cats are good.
an insect/arachnid: Moth still.
a marsupial: Thylacosmilus... probably spelt wrong, internet hates me.
a microoganism: E-Coli.
a mythical species: Generic dragon.
a primate: Human. What?
a reptile: I go for dragon again.
a rodent or lagomorph: Ratty!
an ungulate: Uh... goat?
a mammal in a group not listed above: Your chin.