Girls typing games are really hard to find as most sites are targeting adults and kids, regardless of gender. I have picked 3 typing games that girls will probably like.
Word Games is a really entertaining typing games that most girls will love. You can choose to be the chaser (monster) or the one who is being chased (cute rabbit). The faster you type, the faster your character will move. At the same time, the screen will show your typing speed and number of errors.
A fun rhythm typing game. You have to type the right letter when a letter enters the circles . There are 40 lessons available and you can change its difficulty level. You can also choose different characters and songs.
Typing Expert has a fancy pink color interface which favours young girls. A typing test takes 5 minutes, which measures your word per minute and accuracy. Backspace is disabled. You have to keep on typing even if you made a mistake.