So, this is a question which is probably a little subjective - some people will probably tell you to be careful and never camp, others will say they've never heard of problems (much like when you tell someone you want to use Greyhound buses in North America).
A bit of research seems to say that:
" Amongst the wild animals found in the forests of Georgia the most common are Caucasian antelope, European wild boar, Caucasian goats, mountain goats, leopards and various types of reptiles and amphibians.". Oddly it doesn't mention bears, wolves or feral dogs. To me this would seem to mean that they're in such small populations that they'll be rare. The word "leopards" would concern me far more.
Wikitravel's section on Georgian safety mentions NOTHING of wildlife.
Looking up wolf attacks on Wikipedia, the village of Giorgitsminda, about 40 kilometres from Tbilisi, Georgia had a wolf attack a woman in Feb 2009. Here's an article about the attack, which points out another attack just weeks earlier. However these seem isolated and rare enough to make international news.
This page mentions the wildlife again and points out that leopards have had only a handful of spottings in the last half-century.
Searching for feral or wild dog attacks brings up only the attack made famous in Georgia (USA) a few years back, rare enough to send shockwaves around the world. Sites that talk about Europe feral dogs typically mention Romania (example) and from my experience, that's the only country in the world where I've felt uneasy about them (when a semi-circle of them is closing in on you it raises concerns).
So, long story short, I personally would say: Go for it, but close your tent at night :D