I made the "Bunny Browser" graphic mostly because I have seen similar graphics ("Best viewed with a cup of tea," etc.), and thought it was a cute idea. Of course, I wasn't happy that noone seemed to have a faux browser graphic with a rabbit on it, so I just HAD to create one myself!
Also, I think that every web page looks better when you have a rabbit (other pets and even humans may be used in an emergency) nearby to share the experience with.
When designing this site, I take some consideration about how things will look in different browsers. However, my main focus is do I like the way it looks in whatever browser I'm currently using. I don't have any brand loyalty to a specific browser. I avoid use of frames, and try to stay clear of complicated java scripts that may confuse some older browsers.
If you would like more information about creating a web site that is accessible to as many browsers as possible, you may want to check out The Any Browser Campaign. There are a variety of cute browser graphics there to choose from, if you want to provide a graphic link to the Any Browser site.
If you would like to use the "Bunny Browser" graphic, please ask first. It is a copyrighted image, and should not be used without permission.