Example:
If I load up firefox and go to google and search for something, syslogo then reports "DNS inquire" to every domain that is hyperlinked within my search result from google.
The same is true if I visit any site that has hyperlinks to other domains, syslogs reports a "DNS inquire" to every domain mentioned on that page that is a hyperlink.

Is this normal?

I thought a DNS request is only required when a connection is being established.