The Safari 3.1 beta is probably out on the net somewhere, but what you installed is not the Safari beta, but an update to Webkit.
Safari uses Webkit.
Installing the nightly build of Webkit will modify the Webkit as installed on your computer.
Safari then uses that updated version of Webkit, but Safari itself is unchanged, AFAIK - other than whatever performance changes are the result of updating WebKit.
You won't see version number changes unless you find the Safari beta, or Apple releases an update that changes that version.