Yes it is absolutely safe to drive your Prius without floor mats. The floor mats only prevent mud from staining the carpet underneath. They do not provide any safety features.
Bugs Bunny does drive a Toyota Prius.
The 2001 Toyota Prius has front wheel drive.
The 2012 Toyota Prius has front wheel drive.
The 2014 Toyota Prius has front wheel drive.
The 2003 Toyota Prius has front wheel drive.
The 2011 Toyota Prius has front wheel drive.
The 2010 Toyota Prius has front wheel drive.
The 2007 Toyota Prius has front wheel drive.
The 2004 Toyota Prius has front wheel drive.
The 2013 Toyota Prius has front wheel drive.
The 2009 Toyota Prius has front wheel drive.
The 2006 Toyota Prius has front wheel drive.