If you want to see the raw requests that the storage client is sending to your developer storage, the rather disturbingly named Fiddle Tool is what you are looking for. Normally network monitoring tools aren't going to see traffic to 127.0.0.1, but fiddler has a "magic" URI you can use to allow it to intercept these calls. If you use the address of ipv4.fiddler, then Fiddler will intercept these packets and forward them on to 127.0.0.1. For more info, see Configuring clients.

After talking to David Aiken we realised that there is another step to get this to work. The Azure storage needs to know whether you are calling into real storage or dev storage; this is important as the URI that is generated is different. For dev storage it is of the form http://127.0.0.1/accountname, however real storage is http://accountname.servername/. This means that by default, when you use the fiddler redirection, the client creates an address of http://accountname.ipv4.fiddler/. Fiddler won't intercept this call and even if it did the URI would be incorrect for the dev store. To solve this, you need to use the UsePathStyleUris config option to override this behaviour.

So, your config file will look like this

<?xml version="1.0" encoding="utf-8" ?>
<configuration>
    <appSettings>
        <add key = "AccountName" value="devstoreaccount1"/>
        <add key = "AccountSharedKey" value="Eby8vdM02xNOcqFlqUwJPLlmEtlCDXJ1OUzFT50uSRZ6IFsuFq2UVErCz4I6tq/K1SZFPTOtr/KBHBeksoGMGw=="/>

        <add key="QueueStorageEndpoint" value="http://ipv4.fiddler:10001"/>
        <add key="UsePathStyleUris" value="true" />
    </appSettings>
</configuration>