If you want the Private fenced in area your best bet is single family home located outside of a community.
I am always available for a consultation to introduce you to the different areas.
there are alot that allow dogs however not many that have fences. may have to look at villas. please forward your email address and info and i will forward those properties in which you can have fences.
all the best,
you can also search at http://-www.naplesbeachandhomes.com
We Market Southwest Floroida Properties to the Highest Level
Most probably you will not find a condo like this in Naples. You might be able to find a townhouse/villa type property with a small courtyard but this might not be large enough for your dog. I know it wouldn't be large enough for my puppy :)
However, in your price range, you could find a nice home in a close-in community where they allow fencing or the home already has a fence.
Here is a sample of such homes: http://www.foreclosurenaples.idxco.com/i/5837/Other_homes_200_300
I hope this helps. Call me or email me if you have questions.