I would like to do a multiple regression using correlation coefficients as my dependent variable - is this possible?

Specifically the project is about whether factors like personality, age, gender etc will predict how good a person is at assessing their own performance on a task. So the dependent variable is the correlation between how well they did and how well they thought they did.

I am a bit worried though that the correlations will be clustered up the high end as a preliminary glance at the data collected so far seems to show people are actually pretty good at assessing their own performance. If so, I won't have a normally distributed set of data - does that matter?

If so, what can I do about it? Would you recommend converting the r values to z scores or any other kind of transformation before using in the multiple regression?

Thank you for your help.