Answer:
Yes she really is stupid when she trys to kill the Batman, and trys to impress the Joker but she always fails XD XD
Actully, she's not really stupid ya noe
She can be really smart sumtimes but she is stupid. She just trys to impress Joker but fails sometimes but not all the times. x]
The above are opinions but I'll try to keep to the facts...
Harley Quinn used to be a brilliant Psychologist. The way she did that was to cheat and be smart. And to cheat you NEED to be smart. She plays dumb to keep The Joker happy. If she tries to think for herself she is most likely to get killed. By her psychopathic boyfriend of course. Again to know that you NEED to be smart. Harley Quinn acts stupid to stay alive that doesn't mean she actually is stupid.