Anyone (male, female, or otherwise) can do well in any engineering field if they enjoy applying mathematics to solve real problems.
There are no 'girl' engineering courses or 'boy' engineering courses. There are just engineering courses. If they put in some studying time, anyone can do well.
STILL IF YOU ARE NOT SATISFIED WITH MY ANSWER THEN ACCORDING TO MY OPINION & OBSERVATION :
Umm.. I guess Computer Science?? So many girls go into it (probably after not being able to chose between courses). And Electrical isn't necessarily for boys alone. Its usually said Mechanical is the boy's only course. But it again depends on your interests - even girls take mechanical in cases where they're really into it.
If you have a knack for drawing, try Civil Engg. or even Architecture (ok, thats not engg but still suggested). Mechanical is suggested if you liked physics and stuff.. you'll learn mechanics, thermodynamics, fluids, heat, etc. etc.. its not all engines... again drawing skills are a plus if you take Mech. Did you learn C++ in Class XI/XII? If you liked it and like working on computers, you could opt for Computer Science. Electrical is quite a tough course (according to me atleast) but again interest in it matters. Electronics & Communication is also a course along the same line... other courses like Instrumentation, Biomedical, Biomechanical, Mechatronics, etc. are also available. Check them out too.
As for job opportunities, all the traditional courses (Civil, Mech, Electrical) have almost the same demand every year. But Comp Sci job opportunities vary cyclically - demand is high every 4-5 years or so, then it cools.
Find out what you are good at or what kind of job you want to take up later. Talk to friends/relatives who've taken up engg. Ask at institutes which do coaching for entrance exams. You could look up syllabi of all these courses too. Make the best choice... you don't want to end up studying things you aren't interested in for 4 years!
Innovation, eh? I would recommend either mechanical or manufacturing engineering. The first one you design cool stuff, the second you figure out how to make the cool stuff, both require quite a bit of innovation. Look into them, they are both good options. It really all depends on what you want to do, but in my opinion those are the 2 funnest engineerings that require the most innovation.
There is no "better" engineering for a girl. Look in to any engineering that interests you. You might like programming or electrical engineering since you can do it at home. Get some kits and play, see if you like it.
Industrial Engineering with Product Realization minor or entrepreneurship minor if your school offers them.
Or Mechanical Engineering
Chem Eng, Nuclear Eng, and Electrical Eng all pay more than
Civil, Architectural, or Industrial Engineering,
and not so likely to be "dirty" as Petro Engineering.
Any will provide many opportunies. However there tend to be more girls in bioengineering for some reason.
Stick with two legs, two arms. I know it's innovative but three legs can get cumbersome.
Domestic engineering. Now get to rattlin' them pots and pans!
What kind of engineering is better for a girl who is interested in a little bit of innovation
