No, actually the fact that it was quick formatted improves your chances of a full recovery, since all a quick format does is mark the drive as empty.
The first thing you should do is be sure not to use the drive at all. The more you use it, the more old data is going to be destroyed. Just unplug it until you're ready to run the recovery program. Which takes us to the next topic.
You need to find some kind of data recovery software. Someone else may be able to recommend a product or two. It's been 6-7 years since the last time I used one.
Install the recovery program onto your computer, and then plug the quick formatted drive in. As you might have guessed, you then run the recovery program and point it at the external drive. I can't guarantee you'll be able to do a full recovery, but if you haven't used the drive at all since quick formatting it, you should be able to get nearly everything to everything back.
Is there anyway to recover data on a hard drive that has accidently had a quick format run on it? I was trying to format my external drive and accidentally ran a quick format on the wrong HD. Is it toast?