Hey Jimmie,
Thank you so much for your purchase and I'm glad to hear Tiled works great for you!
You're definitely welcome to redistribute Tiled along with your game, since Tiled is distributed as free software under the terms of the GPL, version 2 or later. You can even distribute a modified version, as long as you distribute it under the same terms (which also means making available the modified source code). Read the license for the full details. :-)
Cheers,
Bjørn