If you use the latest Java7u9 WebView and browse to this dojo example page:
http://dojotoolkit.org/reference-guide/1.8/dijit/form/FilteringSelect.html
you can test some simple dojo examples.

The first example opens a small dojo window containing a single combobox.
After opening the dropdown list of the combobox I have no chance to select
an entry in the dropdown list.
The keyboard cursor keys still control the main webpage instead of the combox dropdown list.
Clicking on entries using the mouse doesn't select the entry.

So it seems to be a focus problem. The webview gets keyboard and mouse events
but does not forward them to the dojo controls properly??

So my current conclusion is that JavaFX WebView is not compatible with dojo.