You can see a sample on Yesterday’s Classics of On the Shores of the Great Sea. It says that it’s for ages 9+, so that’s close for your child, so I’d suggest taking a look at the language and length to see if it’d work for you. It’s also on audio at Librivox.
CHOW is good for her age, too.
Technically, you could read CHOW and have her listen to …Shores…Sea. I don’t know how many chapters are used to cover Greece.
Some books that she’s probably like reading on her own-mine did- are the ones (from Yesterday’s Classics):
Our Little Athenian Cousin of LOng Ago– available at Heritage History: http://www.heritage-history.com/www/heritage-books.php?Dir=books&MenuItem=display&author=cowles&book=athenian&story=_front
Our LIttle Spartan Cousin of Long Ago – http://www.heritage-history.com/www/heritage-books.php?Dir=books&MenuItem=display&author=cowles&book=spartan&story=_front
The Spartan Twins – http://www.mainlesson.com/display.php?author=perkins&book=spartan&story=_contents
also: http://www.heritage-history.com/www/heritage-books.php?Dir=books&MenuItem=display&author=perkins&book=spartan&story=_front
one or two of the Greek mythological books at Yesterday’s Classics.
You couyld also take a look at Heritage History, color coded green for elementary readers: http://www.heritage-history.com/www/heritage.php?Dir=civ&MenuItem=greek