Digital signatures do not create trust; they just move it around and concentrate it. You are right: if you distribute the public key with the package, you have gained nothing.
What digital signatures give you is the ability to handle your trust separately. You still have to find a way for verifiers (the "desktop applications") to make sure that a given public key is indeed the right public key from the authentic signer. But a public key is somewhat shorter (typically a few hundred bytes), can be shared (you can sign several blobs with the same key), and can be distributed in advance (you can "give" the public key to the verifiers before signing the blobs -- even before knowing how many blobs you will ultimately sign).
Public key is not the only source of trust. Indeed, the code within the application which uses the public key to verify signatures on data blobs must also be part of the "trusted realm"; if an attacker can alter that code, he can replace the verification code with something which just always says "that signature is good". Come to that, he could also plant a virus or a keylogger in the application. So not only you have to start trust somewhere, but the problem is not exactly new either.
Therefore we may assume that you already solved the issue of making sure that when a user gets the application on his desktop system, he gets the "right one" and not a maliciously modified variant. There are several ways (e.g. Web distribution through HTTPS; or installation performed on-site by your personal). This leads us to the following solution: embed the public key within the application itself.
Operating System vendors have done that for years, to enable safe system updates. When a Windows decides that it must download and install an update, it actually verifies a digital signature on the update blob before applying it, and it does so relatively to a public key which is already embedded in the Windows code.
(The system can be made more complex with certificates if you want to support key rollover without a software update.)