Can the link title default to the node title?

an alternative to the php code could be automatic node titles module.
This way you can hide the title field and autofill it with the link title

This is a duplicate of link token support: http://drupal.org/node/118255. This feature would allow you to make the title default to many different things, not just the node title.

Oh yes, this could also probably be done with the PHP code block. However, I'm not sure how to use that field yet :)

I'll leave this open if someone else has the answer.

This is what I've done, + it might be what the original poster is looking for.
My content type is set to use no title, then using a custom node template, I use the node title field to construct the link, like so:

<a href="<?php print $field_link[0]['url']; ?>"><?php print $title; ?></a>

Can you show us exactly how that is done and what it looks like?

With the latest development version (soon to be version 1.6) you can combine link.module with token.module to set dynamic titles or URLs. Enable the token module, then configure the settings for your link field. Under the default value you can enter '[title]', which will automatically be replaced with the node title when the node is viewed.