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Welcome to IIS
My suggestion for a beginner visual telescope for your daughter that has both manual operation to find objects and automatic Goto operation ( very easy to learn with Dads help ) and is also light and portable is the Skywatcher 130mm Virtuoso mini table top dobsonian reflector telescope
It’s over your budget of $400 ( at $599 ) but it’s the complete kit with plenty of magnification using various eye pieces for Lunar , Planetary and DSO observing
For an 11 year old it will be an ideal telescope to get started into the hobby and for years to come
Hope others can provide advice as well , but that’s my recommendation
Enjoy this amazing hobby
Cheers
Martin
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