Keep at it. By the time you're done, the existing book will be older, maybe forgotten or in the background, and like you said, your story isn't exactly the same. Don't worry about the similarities for now, just write YOUR story and see if you can get it finished. It's too soon to worry about it being too alike someone else's story. Even if it is, that shouldn't stop you from putting hard work into it.
I put a lot of work into a story once until stopping one day and realizing, it seemed like a blatant ripoff of
Watership Down! o_o;; I'd seen the movie but not read the book, but it was similar enough. I suspended work on that out of terrible embarrassment. But I've never truly given up on it. I know it could be reworked enough so that it's not a knock-off of that story.
If your story is so SHOCKINGLY similar to the one you Googled, then you might need to redirect your attentions, or rework it, so it comes out differently--which is what I would have to do (seriously, I don't have tons of rabbits, and the basic plot is different, but there's an animal quest, and there's a goofy bird with an accent--that's similar enough for me
)--but still, please don't give up on it entirely. It could turn out completely different, you never know. Heck, my story probably would have turned out nothing like
Watership Down at all--except for the big goofy bird!
--she who also has a story featuring rodents in WWII and was stunned to realize that somebody had already done that
