Design and construct a lab scale wetland should be quite easy. In lot of studies there is lab scale wetland with area of only 1 m2, so it is only a small box filled with specific material (it depends on what you want to test) and it's being filled with small pump with sample of artificial wastewater prepared in a lab. I think, that in such case, the testing of the water is more expensive than the lab scale wetland itself..
But there are lot of types of CWs and also there is a lot of things you can test, so I think you need to be more specific with your test hypothesis for developing the best design of the lab-scale CW.
Zhu et al., 2018 Influence of vegetation type and temperature on the performance of constructed wetlands for nutrient removal. https://iwaponline.com/wst/article-abstract/77/3/829/38530
Gross et al., 2008. Small scale recirculating vertical flow constructed wetland (RVFCW) for the treatment and reuse of wastewater. Water Science & Technology 58: 487-494.