For client-side Javascript, I started with JQuery and never really "got the basics" before that.
If you want to build plugins for your Framework of choice (JQuery in your case), then it is also a good idea to understand what is happening behind the scenes.
There are many situations where using a Framework is not really suited. Do you really need to embed your framework of choice (JQuery in your case) if the only thing you need is show or hide a single element of your page ?
I think "begin with a framework or not ?" is a long debate (whatever the language is). I don't have a good answer to this but in the long run knowing the language you use is recommended.