I like the VEX IQ product also over the Lego parts (unless you are sitting on a ton of Lego parts, then go that way).
RobotC is very easy to learn, I've taught dozens of middle school roboteers.
There is a graphical programming package called Modkit that looks like Scratch. Lots of middle school roboteers already know Scratch.
There is some amazing code capabilities with the IQ system since all the motors come with inbuilt speed controls and speed measuring devices.
The add on parts choice is pretty expansive. They come in a number of colors so you can build color coordinated robots. It's important that your robot creation is always fashion forward!
The big Hexbug parts are IQ compatible. You can do some very cool mashups with the Hexbug parts.
As an aside, getting the
4-1 Hexbug kit may also be a choice. You can see in the picture you can mash the 4 bugs into "Left Shark"

But it would let her build robots that work and she can drive around. If she's then into more, get the IQ Superkit and build away.
VEXIQ competitions are all over the place and there are more starting up every year. In the Philly area there were about nine of them this year.
All of the middle schools and high schools in Delaware are switching over / starting with IQ. It's a bigger bang for the buck for them, the teachers that I've talked to really like them.
Pro tips: Buy a small flat blade screwdriver to help pry apart some of the smaller plates.
Watch the tutorials on how to build, they give you lots of great hints. The initial claw / loader robot is easy to build.
Get a small collection of 8/32 bolts in some small lengths with matching nuts. Sometimes you come up with a design that the locking pins can't keep together. (Normally from bad design like trying to keep a long arm on the robot with a single pin). At age 10-11 you can do a quick "bolt it together" to make it work and test it out cycle. Then you can say "Now Uncle JVN would say 'Time to iterate the design to make it better'" and figure out how to ditch the bolt.
Buy some of the Plano small parts boxes (Harbor Freight has them for $3 when you use your %20 coupon) and sort the small parts into them. The Superkit comes with nice dividers that work well with the bigger parts, but being able to pick up a 1x1 connector without digging through a pile of parts is nice. Plus you can boost her "keep things organized" skill set that will make her super popular on FRC teams.
Good luck and have fun!