Suppress some output from PL/SQL script in Toad for Oracle
If you were running via SQL*Plus, you could use set feedback off to suppress those messages.  TOAD supports a subset of SQL*Plus commands so I'm not certain that it would support turning feedback off but I would expect that it would.

Personally, though, I'd strongly prefer moving away from a reliance on dbms_output here.  Whatever you build is going to get screwed up as soon as someone adds a couple of dbms_output debugging commands to one of the procedures that you're testing.  Plus, you're already in a database-- it seems to make a lot more sense to have a test_results table somewhere that you insert data into and then run queries against (i.e. get the count by status) once the test suite is done.  If you store those historically and throw in some timestamps, that gives you the ability to do things like look at performance changes over time and things of that nature.