You've given no thought to exactly what the signature would be over, nor how having one or more untrusted caches between you and the client might affect the content. If you think you can merely sign the payload, not the headers, think again. Where exactly do cookies live? What effect can the status line have on a client's behaviour? Now ask yourself, what are caches allowed to do a request without stepping outside the bounds of the standard? Yes, exactly.
You haven't addressed at all how the client would even get hold of the public key needed to verify the signature. You haven't addressed what the signature is over in the event the server uses some content encoding like gzip, or the chunked encoding. You don't even add the obvious and trivial optimisation that the signature would be best sent as a trailer rather than a header, neither do you define the behaviour if the server wishes to send trailer fields after the HTTP payload.
The only thing that can be concluded from this is that you don't really understand security or indeed HTTP. I'm baffled by the attitude that you admit you don't know anything about these topics, but you're trying contribute something to the field anyway. This is completely arse backwards, and in no other field of endeavour would anyone even consider tolerating it. Would a peer reviewed biology journal look kindly on me if I sent them my thoughts on protein folding? I think not.
The attitude that any software engineer can do security is prevalent in the industry and gets us in to ridiculous amounts of trouble. You wouldn't believe how many software and hardware products I've seen that are completely broken security wise thanks to this. If you're interested in the field, I'd suggest starting by reading the canonical introductory text, Secrets and Lies .(http://www.schneier.com/book-sandl.html) This is not a field anyone is going to thank you if you want to learn on the job.