I am an international student from China. I have a B.S. in statistics, a B.A. in economics and a M.A. in economics of education, and I have very limited background in psychology (I have only taken introductory psychology, social psychology, organizational psychology and educational measurement, 4 courses only), while I was still admitted by several programs in this area.
I think it is OK that you are not a student in psychology, since this field is not that close to other areas of psychology. Do not worry, and you can find that many faculty members in this field do not have a background in psychology as well. Someone even told me that quantitative psychology is more like a program in applied statistics. I suggest you take some courses in statistics, such as mathematical statistics, regression analysis, multivariate analysis, experimental design.
You should think a lot about your own research interests. People in this field are studying a lot of different things: fMRI data analysis, multilevel models, structural equation modeling, longitudinal analysis, causal inference, program evaluation, item response theory, large-scale assessment... Some of these topics are actually not that close to others, but they are all within quantitative psychology.