Is it possible for a favicon icon to be malicious so that you get the virus by just looking at the icon in the search results of a search engine like DuckDuckGo that displays the favicon icons for all the results? Or is the image file so small that it is very unlikely that any malicious exploit code could be in there?
At the moment, no.
Icons are data, not code. There is no mechanism to execute malicious code paths due to the contents of an icon, because icons don't get executed, they just get displayed.
That could change. But it would take a vulnerability to make it so. In that event, the "malicious icon" would be tuned to take advantage of the vulnerability in the software that displayed it.
At the moment, there aren't any of those vulnerabilities that we know of, so the term "malicious favicon" doesn't make sense, as there isn't a way to make one malicious.
That doesn't mean that there never will be, but right now there isn't.