Copyright extends to all work which requires a certain amount of creative work. A PSD file definitely constitutes this, and that of course extends to the structure inside this file with its layers and additional information. Whether any additional protection may need registration somewhere or not, may depend on jurisdiction - usually no such thing is required: you are the author, you have copyright without further ado.
Generally, the author or creator is not bound by any license. They can choose to grant other people certain rights or permissions in using and re-using their work. This is done usually be choosing a license. And they can even give different people different and conflicting licenses for their work.
You are bound by a license attached to a piece of work when it was produced by another person and you like to use it, distribute or incorporate into your own work. Then you may only do that according to the rights granted to you in the license you were given.
As to licensing a website when you are the author and create it from a PSD file: IMHO it is good practise to release the PSD file as part of the source of the website also under GPL. It is one of the intentions of the GPL to be provided with all the necessary sources in order to recreate the result. If the website can be created from a PSD file by choosing the proper script (e.g. by activating select layers and saving certain parts as images in whatever format) or export options, it would IMHO be good to provide this PSD file along with the instructions how to create the website from it as part of the source.
However, as long as you are the author of the website, and you consider only the exported form as source, then there is no-one who can come to you and require you to release your PSD file under GPL, or any license for what it is worth. Yet iff you release the PSD file at all under an open source license, GPL would be a good option, if the resulting webpage is licensed under GPL, too. If you want to release it more restrictively, that's your prerogative, too.