If by reliability test, you mean Cronbach's alpha, that assumes you have a single factor. If you observe a high alpha, that usually means there is little reason to run an EFA, other than to confirm that there is nothing unusual going on.

As for pretesting versus working with a larger data set, a factor analysis generally requires a larger data set (e.g., 10 observations per item) to give stable estimates for the loadings. So, the smaller amount of pretest data is most useful for determining whether a scale does indeed fit the hypothesis of a single underlying factor.

You should do the exploratory study before validity testing

Hi Rajkumar

I second the opinions by David and Fathuma.

Adding to this discussion, EFA is run to uncover a pattern of item loadings on factors or components. Unless, the factors are pre-determined and the items have been used in many previous work, leading to a common conclusion that the items fit (i.e., load) satisfactorily into their known factors/components, you may do away with EFA and consider running CFA (confirmatory factor analysis instead). 

As suggested by David, more observations per item result in more stable parameter estimates. Having said that, authors advise against using the same data set for both EFA and CFA, as this procedure can be harmful leading to a phenomenon known as 'capitalised on chance'. EFA and CFA must be made on two different data sets. 

If you have included a pilot study in your methodology, the data set from this phase can be used for EFA, and run reliability test on the emerged pattern of factors/components. Using this information, you can use the 'template' on a full-scale data set. 

Hope this is helpful.

Saiyidi