 If you liked
Super Doll Licca-chan
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 ...then you might like
Yuusha Exkaiser
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While different genres (magical girl / super robot), both feature a very young protagonist that gets most of the screen time, focusing on day to day life, but does no actual fighting. The fighting is done by (group of) protector(s) that steps in to save the day, then to quickly vanish thereafter.
In both shows, the bad guys are a group of hilarious small fries, led by a pure evil head honcho.