There is a CEF (Chromium Embedded Framework) that currently works with windows and mac, but it doesn't yet work with linux.
As someone running linux, you have two options.
1. Compile and use the qtwebkit plugin from bazukas available
here.
or
2. Open the alert box in a browser window, then use the "Window Capture" plugin to capture just that window. Then crop the capture down to get rid of any window decorations. Then use the "Chroma Key" filter to make the background color transparent.