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Seconding Doctor Who books, especially the new series tie-in books (not because they're "better" but they're more suitable for very young readers, I think). Also, the Eleven Doctors, Eleven stories anniversary compilation that should be released right about now is a great anthology of stories written by eleven currently popular YA and children's authors, and while not all of the stories star girls, many have young female companions.
My other ideas are probably more suitable for sightly older kids due to themes, but I'll mention them anyway in case someone else is looking for science fiction with girl protagonists and these are recent YA books I've enjoyed:
Earth Girl and Earth Star by Janet Edwards (these books have a mild romantic subplot - nothing explicit, but kids that age don't tend to be into romance) - not space-based, strictly speaking, but set on a future Earth with lots of colony worlds and almost everyone being able to travel away from Earth other than the main character and others like her.
Katya's World and Katya's War by Jonathan L. Howard (Katya's World may be suitable, depending on the child's maturity level; Katya's War has some violence of the sort that might upset a younger reader) - again, these aren't strictly space-based though - they take place on a future colony world, but almost all of the action is on that planet and underwater.
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