What is the extension on the file?
Did you change the extension on the file?
Does apache know to parse for perl in files with that extension?
Which file won't it parse, the header or the original page trying to include the header?
Are there any error messages?
Does this describes your idea? Is so then:
Apache cannot parse SSI directives that are in the output of the script. Web-server just sends it (output) to the user. You can solve the problem if you will install Apache 2.0.
With Apache 1.3 you either have to parse SSI directoties yourself (it is easy!) or you may read header.html via http somelike this:
use LWP:Simple;
my $header = get ("http://server.some/inc/header.html");
print $header;
I think parsing file in script is better solution.