In addition to the many good comments in the above material I'd like to suggest a deliberate use of XtremeProgramming. That's just a fancy schmancy phrase for two people working at one computer on a program of mutual interest.
If you daughter happens to be a fanatic on any given subject, such as a singing group or favorite cartoon it might be possible to create a useful script which would serve her keen interest. A database of all known Pokemon might be good for some kids. Or perhaps for a young girl a Barbie's Diary program. For an introduction to programming it might be great fun to do a project with you. But the results will need to be very inspiring.
If you want to get a youngster interested (and capable) at solo programming it might be a good idea to look into something such as Legos robots. They have a fun interface. You can "write" programs to make the robots do things, then download the program into the robot. While this is not a highly developed language it is one you can quickly turn a youngster loose with. This is very similar to the old Turtle program from Pluto (Plato?) days.
For a rather young programmer I think the best approach is to infect them with the delight in having the environment do stuff based on commands written into a "program". For this the loop (and frustration cycle) between command and "cool stuff happening" should be minimal. Later when they are a trifle more developed Perl is excellent.
Have a fun and productive summer,
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