Yep, you can walk along the promenade deck (deck 5), which loops the entire ship, or you can jog on deck 11 near the sports area. It is shorter, but pretty nice. The promenade deck requires some dodging of deck chairs etc, but is a nice walk.
Not sure about Dream but Conquest class ships it is something in 1/11 mile. Hope you don't get dizzy. If you are serious about jogging you might want to get up there early before strollers (like me) start taking up space - or work projects.
All I ask is a tall ship and a star to steer her by; John Masefield
Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012, Dream 2013
Celebrity: Summit 2011
Princess: Ruby 2010, 2014, Caribbean 2013, Coral 2014, Regal 2014
Star Clippers: Royal Clipper 2015