First of all welcome to our happy cat family here on catforum.
Does your cat like the water? I have one who absolutely loves water. Every time we go to have a shower or a bath, or even if the water is running, he is right there like a dirty shirt on wash day.
I too love the picture of her with her mouse.
Actually, the cat that loves water at my place is named Mouse. 8O
Yes, our cat does excactly the same. Everytime we go to the shower she always follows there and hesitates the flowing water. Same with tap water, always playing with the water by her paw. Unfortunately when we wash her she is not too cooperative with that and goes tail between legs position How about your cat when it comes to washing or even swimming?