I'm trying to do something similar but the links don't get updated. Here is my procedure, please let me know what I'm doing wrong:
New:
http://www.jefferyjensen.com/duggal/dw/start
Old:
http://www.jefferyjensen.com/dw/start
1. using GoDaddy file manager, I copy my entire dokuwiki site to a new folder
public_html/dw -> public_html/duggal/dw
2. change basedir or baseurl (I tried changing each one, didn't seem to do anything)
public_html/duggal/dw/conf/local.php
3. deleted everything in cache folder
public_html/duggal/dw/data/cache
References
https://www.dokuwiki.org/faq:servermove
https://www.dokuwiki.org/faq:backup