Ceruloplasmin and copper blood tests are routinely performed in hospitals around the world, as this is used to diagnose copper maintenance disorders like Wilson's disease. Most are simple fluorometric assays, and there are commercially available kits you can purchase.
I strongly recommend you do not use this as a measure of oxidative stress in your system, as altered copper or copper storage does not always mean oxidative stress. Additionally, circulating levels of these copper measurements will not tell you anything about cellular oxidative stress. More established methods for measuring oxidative stress in serum would be TBARS, 4HNE, or EPR for circulating radical species.
Randox website should have some information regarding the kits used to estimate serum copper or ceruloplasmin concentrations. However, in regard to the validity of these tests, I cannot see much benefit in using them for evaluation of oxidative stress. In my opinion, unless you use sophisticated and high-tech instrumentations, the reproducibility of these assays may not be satisfactory for a research project.