If you choose to change the domain name, I would suggest that although it pretty much all comes out in the wash that you should have very valid reason for disrupting an established web site.
So, yes even a low ranking PR3 should be 301'd to the new domain, as yes this will resolve your authority, trust, links and
PR to the new. However, this does not mean your new site will start as PR3.. I have seen some take 6 months to transfer.
The length of time for the transfer of these metrics is very dependent on the "old domain's" authority, trust,and crawl rate. I would advise that you stay very relevant to the old site's theme for the best results and that you immediately begin a good link building campaign for the new domain at launch.
Just a note, most registrar's redirects are not a true 301 and will not suffice for this purpose... Park the domain in your account or leave it where is is if you have the slots and do a proper 301 redirect as a 302 does not cut it.
~Melanie