Yes, you can run CFA separately for each construct (latent variable), assuming it is measured by at least 4 items/each (i.e., df > 0); however, you don't need to do so (also, doing so, you are unable to test the discriminant validity between the dependent variable with each independent variable). If your sample size is large enough, you'd better run CFA for all constructs in your model (called final measurement model or saturated model). Instead, you use pairwise CFA (running every pair of the constructs in your model). This is also good for testing discriminant validity; see Fornell, C. & Larcker, D.F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39-50. for more info)  

Thanks for answering Sir. I have smaple size of 206 respondents. I have acheived model fit by running CFA for single latent variable with df>0 ; but same problem as you have mentioned above; unable to check discriminant validity. Is it necessary to check discriminant validity as there is just a single latent factor? Whether is is acceptable if i proceed with a good fit model (achieved GFA, CFA, AGFI, RMSEA, PCLOSE, SRMR) without checking discriminant validity?