I learnt HTML/CSS a good few years back, then PHP a little later. I\'ve recently become interesting in web development again, just started playing with frameworks like Djang
Yes, jumping straight to framework-based programming instead of DOM is a good idea.
I started doing JS before any major frameworks like jQuery came along, and was reluctant to switch at first, but when I first started using jQuery, it felt so good to be able to write selectors and stuff and not have to worry about cross-browser compatibility.
However, there are some areas of JS where frameworks wouldn't be available. One of them is in userscripting, where you have to make your script work on a site you don't control. Another such one is the use of JavaScript in applications such as XUL.
Overall, I suggest you start with some trivial JS applications, then switch to jQuery instead of going on to the complex topic of DOM.