Correct use of Blockquote, q and cite?

Yes. They are not presentational elements — blockquote represents a block quotation, q represents an inline quotation, and cite represents a reference to a name, work, standard, URL, etc.

You do have some validation errors that are fairly common with blockquote. A blockquote element cannot be inside a paragraph, and in HTML4 actually needs to contain paragraphs. The nesting of the p and blockquote elements in your fragment needs to be reversed.

The blockquote element (also the q element) can optionally have a cite attribute to specify a URI where the quote came from. HTML5 says user agents should make that link available to the user, and HTML4 doesn't say anything at all. I would include the URI both in the cite attribute and as an inline link, since browsers don't handle it.

Here's how I would write that fragment, with those revisions in mind:

<blockquote cite="">
  <p>Type HTML in the textarea above, <q>and it will magically
  appear</q> in the frame below.</p>
  <cite><a href="">reference url</a></cite>

Validate this fragment