Yes a stabilizer will help but will not solve the problem. Adding weight will also help. A better solution, build a smaller (shorter) wing. Try removing 10 inches, 5 from each side.
The MT1806 2280KV will easily cope with a 3s 1000 mAh, but Ive upgraded my last build with the mt2204 2300KV motor its much better for the 4ch version and cheaper too.