Although my iPad has replaced my netbook, your question about multitasking suggests you may be disappointed. The iPad's multitasking capabilities are quite limited compared to a full fledged computer. You can certainly listen to music while editing a document, for example, but you cannot watch a movie while doing so. (Even if you could, I doubt you could enjoy the movie or do justice to the document.)
Furthermore, I suspect you'll find that you may have to add a bluetooth keyboard to the iPad and opt for at least a 32 gig/3G model to support your requirements. For that price you can certainly purchase a highly capable netbook with better multitasking capabilities, a better browser, and a larger (say 11"), denser (1366x768) screen.
The iPad's battery life is likely to be better than a netbook (mine certainly is.) On the other hand, you indicated that the battery life on your netbook has declined significantly over the last year. You might want to consider replacing the battery in your netboook rather than purchasing a new device.
On the other hand, the iPad offers features that all but the most expensive ultraportable laptops cannot match, the most important of which is the touch screen interface and the functionality (e.g. handwritten notes) it supports.
In short, you can replace a laptop (and certainly a netbook) with an iPad. But it will involve compromises and depending on your requirements, it may not be an economical alternative.