Josh, if you aborted the connection, you are safe. Yes, malware would have downloaded without the shield. (Whether it would have done any damage on an up to date system is another matter, and beyond my knowledge.)
Oxydose, I have the latest Java version also. Yours is a version prior to mine, but has no known vulnerabilities. (Update if you wish, but no urgency, I think.)
The reason I got no warning initially is that I use the Noscript addon. Suspending it produces the Avast alert.
I have contacted the site with the information about the exploit.
Just goes to show you (assuming this is not a false alarm, generally a safe assumption with webshield warnings): sites can be hacked. The web can be a hazardous place.
(And Avast rocks!)