Hello,
I have a vast amount of experience building applications that use embedded browsers especially Webkit, as proof of this I can provide links to applications I have done that do this as well as links to multiple patches that I have submitted (and had accepted) to Webkit itself. Contact me if you would like to see these links, as I am not sure if I am allowed external links inside a bid here. I also have a vast amount of commercial C++ experience where I have developed projects independantly so I know how to estimate time properly, I am 100% confident in my estimate.
I can do this task for you in a quick and satisfactory manner. We would need to discuss your needs in a bit more detail however, as 'Webkit' itself is not something that can be used directly (think of Webkit as a meta project) - it would be necessary to decide on a port of Webkit to be used (e.g. There is a 'qt' Webkit, a 'gtk' webkit, a 'wx' webkit, until recently chrome Webkit, Apple Webkit etc. etc.) so we would need to discuss which of these is actually going to be best for your project and meet your requirements best...