A number of companies are working on various Internet tools for the BeOS, but it sure wouldn't hurt to ask Quarterdeck about their product plans for the BeOS ;-).
You can give feedback to Quarterdeck/Star*Nine by sending them mail at email@example.com.
In the meantime you might want to check out the port of Apache to the BeOS, Zorro from LittleBig Software Engineering or diner from stegemann & stegemann.
Read more about the Apache port here:
You can read more about Zorro on the LittleBig web site:
You can read more about Diner on the stegemann & stegemann web site: