You should probably have a look at modperl.
(http://perl.apache.org/)
There's also a book available for free: http://modperlbook.org/

Modperl will compile your perl scripts only once, and answer all requests with the already compiled scripts.

Update:
To go more into the details:
It's hard to say what needs 3 seconds, without having more data/the code.
I could think of:

• Perl needs some time to compile the packages
• Perl needs so long in order to find the package
• The database connection is established while requiring the packages, this could also take 3 seconds

However, all of the points above could be solved with modperl,
the database connection could also easily be made persistent.(Apache::DBI)