Do you have a my.cnf file in /etc ..??
what does the "socket" value in the file say..

If you do not have a /etc/my.cnf create one with the following values.
This is the sample configuration on my machine

[client]
socket=/tmp/mysql.sock

[mysqld]
port=3306
socket=/var/lib/mysql/mysql.sock
set-variable = key_buffer_size=16M
set-variable = max_allowed_packet=1M

[mysqldump]
quick

Here is typical user option file:

[client]
# The following password will be sent to all standard MySQL clients
#password="password"

[mysql]
no-auto-rehash
set-variable = connect_timeout=2

[mysqlhotcopy]
interactive-timeout
[download]

Once you write the file, restart Mysql and try connecting to the Database using

mysql -u plankton
[download]

If the above command succeeds then you need not worry about connecting to Mysql using Perl

Hope this helps

Good Luck!