There's no way (at the moment) to include remote images in with the pasted HTML. I can make it option in the settings as the HTML paste was an initial request from some other users who didn't want images but wanted some formatting.
At the moment, until the feature is implemented, the way to get an image into the Document would be to RightClick+"Copy Image" from the web browser, than paste that into the Document. Or you could use the "Capture Part of Desktop" from within doogiePIM.
Warning; Having a feature to download and include all images from a pasted HTML will result in having lots of unnecessary images in your content - such as buttons, clipart etc. This would inflate your document database size for little reason. I would say it's better to be selective, but I will implement the feature in a future version.
Do you really need all that HTML format and images?