Lucky☆Star, Kitakubu Katsudou Kiroku Recommendations
Both anime have only female leads. There is no actual plot, instead each episode is separated into short segments of different unrelated stories. Both are slice of life.
Both slice-of-life. Both talking about random things then turns into something crazy and hilarious. Both having this cute 'filler' pet. Both shows ranting about something similar. Uses parody.