I think the easiest method would be to use Advanced Prev Next Entry.
entry_date vars are in fact available in this tag pair. I know because I just tested it for you :)
{exp:channel:entries channel="blog"}
{exp:bbr_prevnext_entry current_url_title="{segment_4}" channel_name="blog" orderby="entry_date" sort="asc" cycle="yes"}
<a class="prev" href="/blog/{entry_date format="%Y"}/{entry_date format="%m"}/{prev_url_title}/">Previous</a>
<a class="next" href="/blog/{entry_date format="%Y"}/{entry_date format="%m"}/{next_url_title}/">Next</a>
{/exp:bbr_prevnext_entry}
{/exp:channel:entries}
Use this and forget about having to mess with turning on PHP or using a second add-on ;)
Note: make sure your orderby and sort are set the same on your listing page as they are set in the bbr_prevnext_entry params (or rather vice versa) other wise things could appear out of order.
Bonus: APNE allows you to do a full circle with your entries via the cycle param. Not something that comes standard with core Next/Previous Entry Linking tags to my knowledge.