If you have JExplorer's Browser object embedded and you're trying to get the doctype from there, you should be able to do the following:

browser.getDocument().getDoctype()

This method returns an org.w3c.dom.DocumentType, which you can then you can make various calls on like getName() or whatever.

To the best of my knowledge, you won't be able to tell from the docType by itself whether or not the page is using AJAX.

I hope this helps.

Ken