really its a decision about whether your test measures what you want it to measure. So you need to have a very good idea of the putative construct, there may be many other scales attempting to measure this as well.
Strauss, M. E., & Smith, G. T. (2009). Construct validity: advances in theory and methodology. Annual Review Of Clinical Psychology, 5, 1-25. doi: 10.1146/annurev.clinpsy.032408.153639
and the classic:
Campbell, D. T., & Fiske, D. W. (1959). Convergent and divergent validation by the multitrait-multimethod matrix. Psychological Bulletin, 56, 81-105.
MTMM is complicated but is the best way. However, before investing in such a hude endeavor I would establish inter-item reliability (Cronbach's), then establish discriminate validity with individual difference measures that are "like" the one you created by just using correlations.
Based on solid Model or Theory then through your panel of experts to validate Face, content and concurrent. Next step should get Factorial analysis process on your construct Q as well as Reliability process. TQ
Construct validity is the degree to which a test measures the meanings it gives and is one of the three main types of validity evidence, along with content validity and criterion validity; thus, construct validity is the primary concern of validity research; being the adequacy of inferences made on the basis of observations or measurements (often test results), specifically whether a test measures the intended construct. Construct validity examines the question: Does the measure behave as the theory says that a construction measure should behave? and it is essential to the overall perceived validity of the test.
The evaluation of construct validity requires that the correlations of the measures be examined in terms of the variables known to be related to the construction. This is consistent with the Multi-Trait-Multi-Method Matrix (MTMM); However, there are other methods to evaluate construct validity: It can be evaluated through different forms of Factor Analysis, structural equation modeling (SEM), and other statistical evaluations. It is important to note that a single study does not test construct validity, as it is a continuous process of evaluation, revaluation, refinement and development. Correlations that fit the expected pattern contribute to the evidence of construct validity. Most investigators attempt to test construct validity before the main investigation; For this, PILOT STUDIES are used, which are small-scale preliminary studies intended to check the feasibility of a large-scale test and establish the strength of their research and allow them to make the necessary adjustments. Another method is the known group technique, which consists of administering the measuring instrument to groups that are expected to differ due to known characteristics. The hypothetical test of relationship involves logical analysis based on theory or previous research. Intervention studies are another method to assess construct validity and are used in a group with low scores in construction, it teaches them construction, and then they measure again the construct validity with different tests. If there is a noticeable difference between the post-test and the pre-test, which are analyzed by statistical tests, then this can demonstrate good construct validity.