“Given that she can only produce one fawn a year..”
They can have as many as four, but three is common and twins are the rule for adult does.
Doe fawns will breed at just over 6 months old and have a single fawn the next spring.
The point really is that a male may be breed with 20 females...so using your stats, cutting off his 00’s would be even more successful in cutting down the population.