It appears to be a pretty obscure book. It's on Amazon, but there are no descriptions or reviews. From the cover, I'd say it was a kids book, which would put it in a different market.
Let's assume that this short story of mine is fit to publish, for arguments' sake, because otherwise I certainly don't mind the duplication. I suppose what this boils down to is: will the publisher care?
It depends.
For example, type "Time", or any other such common word, in Amazon. You will find there is more than one book with that exact title. Certainly, when searching for books, I have found many books with the exact same title. In such cases, I use the author or genre to narrow down my search.
On the other hand, if the book is in the same genre, then it would matter, although again, maybe not so much.
In your case, since you say it is a different market, I would say don't worry about it. And in any case, the publisher might change the book's name anyway, because they feel they can market it better with a different name. If they feel the title duplication is a concern, they'll change the title.
So I would say go ahead and use the title, and let the publisher worry about any name clashes.
Edit: In view of @One Monkey's comment below; if the title is similar to another book, make sure it is not similar to one by a best selling author, or a famous series. So if you choose The Hobbit, or Rendezvous with Rama, you will be in trouble.
I'd say that it doesn't matter at all.
Titles are not required to be unique. A little searching can reveal dozens of short stories and novels that have shared titles, all without hurting recognition or sales. I would only be concerned about this if one of two things apply:
I've had the same feeling in regards to my "Metaverse" in my ongoing book "Legends of Wind". If you enter Metaverse into Wikipedia, you can see that it is not a new word. My definition is different of course, but one other definition, for example, is the merging of this world and the internet, where they blur together. It has also been called upon for an obscure virtual world of roleplaying. I'm sure there are others as well. My point is that there are only so many original ideas out there, and given variations. Some of them are going to bump heads. As long as people don't become stingy with them, there should be no problem, within reason. Obviously, talking about "Sparkling Vampires" and titling your book "Twilight: Second Moon" will raise more than a few eyebrows and will probably result in a lawsuit involving copyright infringment. But, by that same token, nobody holds exclusive rights to the idea of the "Vampire" or the "Werewolf". You can be creative enough to make your own variations. If not, then just write fanfiction with the usual disclaimer. It's all in good fun.
If it is obscure and not in the same market or was published long ago it probably wouldn't matter. If you are aiming for something higher though and want to minimize potential problems with publishers you can rename the book to something else.
