Answer: You can prune in June or you can prune in the winter months on a day when temperatures are above about 45 degrees. I would however caution you against removing larger branches as this can open the tree to attack by pest or disease. Also, do not remove a substantial portion of the branch structure all at once as this can encourage growth of excessive water sprouts.
Rabbits can sometimes be repelled with the spray on or granular repellents labeled for rabbits (read and follow label directions for when to apply/reapply) or by sprinkling blood meal on the soil (keep it away from the berries, reapply after rain). In the long term however you may want to consider a wire mesh fence to keep them (and other animals) out of your berry patch or vegetable garden.
Q&A Library Searching Tips