Will low light scope work for night shooting?

We have nutrias in our lake we are trying to get rid of. I got a gamo whisper air gun but the scope doesn't really work very well for night shooting. Most of my shots will be less than about 50 yards or so since I am usually shooting at a swimming nutria. Anyway, I am newb at any gun related and was wondering about scopes. I really don't want to spend $500+ on one of the "true" night scopes so I figured I would ask folks here on the forum if a "regular" low light scope will work for me. I have found that there is enough light that I can see the nutria just fine with a small set of binoculars i have . Big difference between the binoculars and the as-delivered gamo scope. I was thinking i could probably purchase a lower-priced (less than $100) low light scope that might work.... Any help folks here can give me would be VERY much appreciated!
 
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My night time pesting....I absolutley need more than just a low light scope. My cheapest set up is my green light attached to the scope. Works great for me out past 50 yards easily for visibility. 

I don't have that scope anymore, but I still use the light...