That's a good question. Is the google search there tied to Browser, or does it just try to go to
http://www.google.com/?p=searchwahteverwhatever.... it could be tied to browser, or it could just try to open the link, in which case it WOULD be possible to use Dolphin with it.
If you haven't done this already,
Home > Menu > Settings > Applications > Manage Applications > Browser > Clear Defaults
Then try your Google Search. If it is possible to have dolphin work with this, it will ask what you want to use for default. Check the box that appears below your Browser choices (Dolphin and Browser will be your choices, you'll see), and then, obviously, touch 'Dolphin'.