This serial is about a boy and girl who got an alien baby along with a talking cat-like pet... If I am remembering correctly the girl's name is Miu, not sure of that. At first they hate each other and argue about household chores but as they grow up they fall in love and at the finale the baby comes as an toddler/teenager to find them living happily...
It must be UFO Baby. All the plot-points matches. Her name is Miyu. Its based on Manga. Here is a picture from it
I have watched it by myself, so i can insure it that it has last episode where UFO baby comes again to see that the girl and boy is now together and have there own same face child.