Ok, here's an oldie. It was aired on the USA channel in the early to mid 80's, and was called Honey Honey.

It takes place in a European country. A handsome masked male thief steals some important jewel and hides it in a fish. The fish is eaten by Honey Honey's cat. So the thief wants to get the jewel out of the poor cat, even if it means cutting the cat open. But the thief has a boy cat that really likes Honey Honey's cat, and often foils the thief's efforts to get the lady cat.

The princess of this country also knows of the cat and jewel within, and wants the jewel back.

Honey Honey (very typical innocent and bubbly cute girl type) spends most of the series (at least the season I saw) fleeing from country to country with her kitty, so it doesn't get cut open.