Menagerie - a moral dilemma

I am beginning to suspect I live in a menagerie. At 05.00 this morning there was a rustling in the wall near my bed - do I want to know what it was? We have had birds come down the chimneys and get between the plaster and the stone in the ancient walls!
Then when I opened the shutters and stared out to our garden there were three rabbits on the lawn and four magpies on the patio! There was also a large fat pigeon in the tree and a grey squirrel on the wall! Lovely I hear you say imagining my ideal rural existence.
Now as many of you know we have two dogs. However they are quite useless at deterring the rabbits. The little one is a deaf and rheumatic temperamental old westie and the big one, a young Labrador, bounces around wagging his tail and is every animals friend!
The rabbits are the ones that are destructive. Last year everything I planted in my vegetable plot was eaten very quickly and not by me. This year I have invested in a fence of chicken wire to keep them out and the beans and courgettes have survived so far. But my main worry is the habit rabbits have of multiplying - like rabbits... so a month from now how many might there be.
My vegetarianism isn't based on absolute principles of never harming animal life but on the clear health benefits and the damage to the earth caused by too much consumption of meat. However, I may soon be faced with a moral dilemma if I ask my neighbour to borrow his air rifle!
I would not hesitate to take the necessary steps to get rid of mice from the house, or a wasps nest or slugs but rabbits are furry and cuddly but they do eat anything that is green. If I could think of a way to get them to eat grass only then I could save on lawn mowing!
Perhaps I should get a great big tom cat that likes rabbit for his tea!
If you start asking moral questions then it can make life very complicated. But if we never ask moral questions and instead go along with what is allowed then we can become like the many members of parliament who have made disgracefully excessive claims on their expense accounts!