Shibani, yes the law gives property rights to the girls, but as you said, no one follows it. And that's because we are brought up in a culture where the tradition is that property goes from father to son. If you think the tradition of lena dena has come off age, then this tradition of not giving property rights to the girl has also come off age. There are communities in Kerala where no lena dena happens as all the children, boys or girls, get equal share of the property. This is not the case in most North Indian communities and Jats are no exception. If the sheer amount of money that exchanges hands on the wedding day is a parameter, then Jats would be much lower in the list. There are communities, where it is a norm to have a rate list based on groom's qualifications. Indian society is in middle of a materialistic revolution where showing off is part of the game. And Jats are no exception.
Personally, I think one can never give too much to a girl, if you compare it against what is legally hers and not being given to her. Your line about biggest gift being education and good morals is a sort of truism, a feel-good abstract thought. In practise, the worst of guy, even one who beats up his parents, gets the property while the girl doesn't. And if anything, even in education or nutrition, most parents tend to focus on the male child more than the female child.
If the question is about how far Jats have progressed vis-a-vis treatment of women, then things like what chores males help in are important but nothing compared to the elephant in the room, property rights, that no one wants to talk about.