Shell Programming and Scripting

I have a group of getOSinfo.out files that I would like to list the filename and then its contents out to. I can do it for each one individually, but would prefer to do it all in one shot and have one large file that has all of the oslevels and filenames. I am not very handy with scripts, so I was wondering if anyone had a script that did this already. It is on AIX so ksh is prefered, but I can probably tweak most things to work. I would like the output to look something like this:

Filename.out
content line 1
content line 2

You get the idea, I am still in my scripting infancy so please bare with me. Thanks for any help with this.

BTW this is what I was using, I know I will need a much more robust set of commands than this.

ls *.GetOSInfo.out > OSInfo.out | cat *.GetOSInfo.out >> OSInfo.out

Code:

for filename in *.GetOSInfo.out 
do
        echo "Contents of file: $filename"
        cat $filename
done;

I knew it had to be very simple. Thanks for the script, I feel like a mental midget when stuff like this comes up. Like I said I am still in the crawl stage of scripting. Hopefully will be walking soon.