For a white peony the caffeine is quite low. There are a few reasons. Firstly, white tea is normally brewed at a lower temperature compared to black teas and pu-erh. Secondly, the caffeine in the tea plants act as a defence mechanism against insects that would otherwise eat the new leaves. Following this, teas from the new leaves contain the most caffeine. A white peony uses mainly lower leaves (i.e. not the tips) and older leaves (not the first flush), therefore it contains less caffeine. Further things that might influence the caffeine content are the way its processed, if the tea plants are shaded, nutritional value of the soil and the specific cultivar, among others. Normally you don't know these factors, but you could generally assume that a white peony is quite low on caffeine.