When I am sharing a URL which have 301 status code with Location header but I found that Facebook didn't fetch contents from destination page but when I share URL of tinyurl.com facebook fetch all contents from destination page and this url also have 301 status code Location header, I also want this facility on my URLs.
You will have to lint your URL at https://developers.facebook.com/tools/lint and fix all errors and warnings listed.
You can lint tinyurl's fine as long as the target location is good. Here's an example of linting a tinyurl:
http://developers.facebook.com/tools/debug/og/object?q=http%3A%2F%2Ftinyurl.com%2F6weoofy