"Gossipy" is the adjective. For "Gossip Girl", it's merely a descriptive term but not necessarily an adjective, same as "United Nations Ambassador" or "Wal-Mart Employee".
Or see it this way: "Ambassador of the United Nations", "Employee of Wal-Mart", "Girl of Gossip".
I think you're asking if "gossip" can therefore be applied as an adjective to other words, but this is not so. Use "gossipy".