Yes! She is like Tripod. She is curious and hopes to befriend the woman who saved her.

[Which would be the other character, the 'strong but lonely woman' who is definitely not Rey. Original character, do not steal. Elleru launches excitedly into an explanation.]

What it is that happens is that she is a normal cat who is cornered by hungry, wild beasts. The woman then appears and protects her, but she is bitten and injured. That night, the cat makes a wish that she can help repay the woman, perhaps by tending to her wounds, and she is transformed into an upright.