Magnetic domain structures are a fascinating area of study with interest deriving both from technological applications and fundamental scientific questions. The nature of the striped magnetic phases observed in ultra-thin films is one such intriguing system. The non-equilibrium dynamics of such systems as they evolve toward equilibrium has only recently become an area of interest and previous work on model systems showed evidence of complex, slow dynamics with glass-like properties as the stripes order mesoscopically. To aid in the characterization of the observed phases and the nature of the transitions observed in model systems we have developed an efficient method for identifying clusters or domains in the spin system, where the clusters are based on the stripe orientation. Thus we are able to track the growth and decay of such clusters of stripes in a Monte Carlo simulation and observe directly the nature of the slow dynamics. We have applied this method to consider the growth and decay of ordered domains after a quench from a saturated magnetic state to temperatures near and well below the critical temperature in the two dimensional dipolar Ising model. We discuss our method of identifying stripe domains or clusters of stripes within this model and present the results of our investigations.