The solution is pretty simple, I think?
It does not matter what choice you make:
Option A) If you shoot him, you will die anyway (because of old age) and your family will also die eventually (because of old age)
Option B) If you decide to not shoot him, you will die immediatly/soon due to starvation assuming you can not find any food or return home, and your family will also die eventually (because of old age)
Conclusion: Shoot the rabbit and eat it (Option A)