In my humble opinion, it's transparently obvious that the author has recently gotten herself a pet cat -- and is adamantly decided to turn every little detail of her interactions with her cute kitty into a yuri fantasy manga story.
By that logic, we'd have to assume she also got herself a hamster at around the same time. Which would be a pretty risky combination, if you ask me.
However, I did a little searching on Neji's Twitter to see if I could confirm your hypothesis, and found several photos of Mick the cat... but sadly he's not hers. (We can probably assume that she's writing from experience, though.) He's no "spring chitten", either, ahaha....
Well, anyhow, as an apology for that terrible pun, here he is in drawing form.
And while I'm at it, here's a cat-related bonus featuring the hard-working Wani-san, who's clearly a reptile of discernment.