You can normally log in the /var/log/qpsmtpd/current log or /var/log/qmail/current log but because these get rotated I doubt it will have the date you requested, only other option is if you enabled BCC copying feature which archives the emails then you could look there. BCC is not enabled but default BCC is disabled.
Although it rotates it should keep some history, I have a lot of older log files still available on my server.
How about this from the SME Server shell:
grep -i 'to email address' /var/log/qpsmtpd/\@* /var/log/qpsmtpd/current
Once you located the proper logfile you can do the following:
grep -ih 'to email address' /path/to/logfile | tai64nlocal | grep 'yyyy-mm-dd'
(Replace the y, m and d values for the proper date values.)
Edit: removed duplicate pipe symbol in last command