...
print SQLP "\@$script_name; \n" or die "cannot write in doScript"; 
# add:
print SQLP "exit\n" or die "cannot write exit to sqlplus in doScript";
close SQLP or die "cannot close in doScript"; 

...

****** Start  t.sql 
  select sysdate from dual 
  / 
****** end t.sql
...