What you've describe isn't really a "unit test" anymore, as you are testing more than just the single unit of your class that uses WebServiceTemplate in isolation. A good unit test of this class would probably involve mocking the WebServiceTemplate class so that you can test how your class behaves when the WST returns different types of responses, exceptions, etc.
For a test that verifies how your class behaves at runtime with wired-up collaborators (and a Spring context), you should check out Spring's TestContext Framework. This allows you to annotate your test classes with things like @ContextConfiguration({"path/to/spring/xml"})
to have Spring instantiate an ApplicationContext prior to running your test, and inject any @Autowired
properties into your test class.
A final note: testing your webservice-using classes against a live web service is typically a bad practice, as this introduces outside dependencies on your tests - is the service up and running? What server is it on? What version is it at? etc. You may not want to run these tests as a part of your normal unit test suite.