A catalytic ozonation advanced oxidation process (AOP) with a copper(II)-doped carbon dot as catalyst, Cu-CD (using L-cysteine and polyethylene glycol (PEG) as precursors and passivation agents), was developed for textile wastewater treatment (T = 25 °C and pH = 7). Four dyes were analyzed—Methyl Orange (MO), Orange II sodium salt (O-II), Reactive Black 5 (RB-5) and Remazol Brilliant Blue R (RBB-R), as well as a real effluent from the dying and printing industry. The Cu-CD, with marked catalytic ozonation properties, was successfully synthesized by one-pot hydrothermal procedure with a size of 4.0 nm, a charge of −3.7 mV and a fluorescent quantum yield of 31%. The discoloration of the aqueous dye solutions followed an apparent first-order kinetics with the following rate constants (kap in min−1): MO, 0.210; O-II, 0.133; RB-5, 0.177; RBB-R, 0.086. In the presence of Cu-CD, the following apparent first-order rate constants were obtained (kapc in min−1) with the corresponding increase in the rate constant without catalyst (%Inc): MO, 1.184 (464%); O-II, 1.002 (653%); RB-5, 0.709 (301%); RBB-R, 0.230 (167%). The presence of sodium chloride (at a concentration of 50 g/L) resulted in a marked increase of the discoloration rate of the dye solution due to generation of other radicals, such as chlorine and chlorine oxide, resulting from the reaction of ozone and chloride. Taking into consideration that the real textile effluent under research has a high carbonate concentration (>356 mg/L), which inhibits ozone decomposition, the discoloration first-order rate constants without and with Cu-CD (kap = 0.0097 min−1 and kapc = 0.012 min−1 (%Inc = 24%), respectively) were relatively small. Apparently, the Cu-CD, the surface of which is covered by a soft and highly hydrated caramelized PEG coating, accelerates the ozone decomposition and dye adsorption, increasing its degradation.