I have a default judgement for $6,369 against a renter that abandoned our rental property and caused damage. I'm thinking about using a company called Judgment Collections of Georgia LLC to collect on the sum owed,but I'm concerned. They are wanting me to sign the judgment over to them for a $1 and give them exclusive rights to collect at their discretion. Does this sound right?

I've run across schemes like this before. It looks like they are thinking that taking an assignment would be a way to avoid the requirement that they hire an attorney.

What would you get out of it, besides the dollar?

Not any agreement I would sign. Basically you are selling it to them for a dollar, and unless there is a agreement of a percent of payment if they collect.
How old is the debt ?