Understanding and controlling the motion, stability, and equilibrium configuration of ferroelectric domain walls is key for their integration into potential nanoelectronic applications, such as ferroelectric racetrack memories. Using piezoresponse force microscopy, we analyze the growth and roughness of ferroelectric domains in epitaxial thin film Pb(Zr0.2Ti0.8)O3, driven by the electric fields at straight edges of planar electrodes at two different temperatures. This device relevant geometry allows us to confirm that the domain walls are well described as one-dimensional monoaffine elastic interfaces driven in random-bond disorder. However, we observe a progressive increase in roughness as initially flat domain walls move through the disorder landscape, which could prove a significant limiting factor for racetrack-type memories using ferroelectrics.