Sore Ike! Anpanman: Yumeneko no Kuni no Nyanii (2004)

When a comet that comes back once in a hundred years, Dream Suisei, is travelling by Earth, everybody sees the same dream of a foreign world. Melonpanna saves an egg from being crushed and wakes up to find out that the egg has followed her home. A kitten hatches from the egg, and Melonpanna names her Nyanii and starts caring for her. But soon they find out that Nyanii is needed back on Dream Suisei, and if she doesn’t return there, she will vanish. Melonpanna struggles with the upcoming hard goodbyes, but the real trouble starts when Baikinman accidentally awakens the evil monster Muuma.

Source: www.anisearch.com/anime/5331