By default Safari hides its built-in developer tools. If you don't have a Develop menu shown in Safari it needs to be enabled. If you do, jump to step 3.
Open the Safari menu and select Preferences...
Enable the developer menu in the Advanced tab
Click the Advanced tab in the Preferences window
Check the box for Show Develop menu in menu bar option
Close the preferences - the Develop menu will now be shown
View the resources the page has loaded
Select the Show Page Resources option from the Develop menu.
The developer console will show at the bottom of the page
Reload the page so Safari can capture all network requests
Details about the Ajax request are shown.
Safari will show a list of all resources (images, scripts etc) which have been loaded for the page. Locate the Ajax request that has been made to the server and click it. Safari will show detailed information about the request.
Note that on pages with a large number of resources, Safari will group the resources by type into folders. If this happens on your site, look for the "XHRs" folder for the Ajax requests.