The content deemed acceptable for Japanese children generally differs from the concept in other countries; manga contains all genres of stories, so one cannot responsibly presume that just because a title was marketed at Japanese kids, that you would likewise consider it appropriate for your kid of the same age.
As one example:
The popular girl's series Sailor Moon was published in the manga magazine Nakayoshi, which was marketed toward elementary school-age girls (1st through 6th grade). This series includes strong language, bullying, violence, death, war, genocide, refugees, lovers' suicide (more than once), non-consensual kisses (forced while awake, while asleep, while drunk), a father fondling his adult daughter while brainwashed, human/animal romance, demonic-style alien possession of human bodies, nudity, cross-dressing, a non-monogamous lesbian couple, and non-graphic sex resulting in teen pregnancy (the 90s anime version, also marketed toward children, also added wrist/ankle restraints for a rape-like, pain-inducing entering of victims).
There are many manga reviews on the web, including those that specifically for parents and teen/preteen/kid readers on what sort of possibly objectionable content is included in the title (such as strong language, violence, nudity, gender-bending, innuendo, sexual content, etc.) and what sort of general content you can expect (for example: horror, potty humor, serious themes like depression/body image/sexual orientation/prostitution/parental abandonment/bullying/suicide) and let you as the parent or the reader use your own judgment about whether a title fits what you deem appropriate at what age. Browsing reviews also allows you to seek out titles that reinforce and contribute to your family's values (such as traits of selflessness, generosity, celebration of uniqueness, etc.).
Some good starting places are:
Since you have a daughter, she may be especially interested in shoujo manga, which was written with the target audience of Japanese girls. Within shoujo, nearly all genres of stories are included; some titles are very cheerful and innocuous and teach a moral-of-the-day, others are dark and heavy. Good starting places to get informed are:
Some shoujo manga review sites are:
More general review websites include MangaBlog and Kuriousity, and a Google search will find you many more.