If I have a PR 3 website, and I use a 301 redirect to a brand new domain, will it transfer all the link juice to the new domain so it would be a PR 3 aswell?
Technically it should but there's no guarantee all your link juice will be transferred if you move your website.
I wasn't completely sure myself, but I confirmed at the following URL that some of the pagerank is lost... http://www.seroundtable.com/archives/021832.html