You're suffering from buffering.
All you need to do is add
$| = 1 before your print
statements to force perl to output immediately instead buffering and
waiting for newlines.
From perlvar $OUTPUT_AUTOFLUSH:
HANDLE->autoflush( EXPR )
If set to nonzero, forces a flush right away and after every write or
print on the currently selected output channel. Default is 0 (regardless of
whether the channel is really buffered by the system or not;
$| tells you only whether you've asked Perl explicitly to
flush after each write). STDOUT will typically be line buffered if output
is to the terminal and block buffered otherwise. Setting this variable is
useful primarily when you are outputting to a pipe or socket, such as when
you are running a Perl program under rsh and want to see the output as it's
happening. This has no effect on input buffering. See getc
for that. See select on how to select the output channel. See also IO::Handle.
Mnemonic: when you want your pipes to be piping hot.