Hi,
it seems to me that the documentation is misleading. There is no parameter in DSA called public exponent. I believe that 2^16 + 1 is a prime number so I guess that they are talking about parameter q. You could verify this generating a private key in Archivelink and exporting it. Inspecting the file should give you an answer for your question. Anyway, seeing key length 1024 and MD5 does not radiate confidence.
Cheers