Unfortunately, you are going to have to send the e-mail from your Quick Office app (or any app, for that matter).
Apple has developed a "sandbox" iOS, in that no app can truly access another. So, the Mail app cannot go to your Quick Office app and grab a document for e-mailing. Actually, it can't go to any app to get something for mailing.
What you have to do is be in the app from which you wish to mail something. In that app is [usually] a button/icon/way to e-mail a file. This will bring up your e-mail as a pop-up, into which you can put your information (TO, subject, message, etc.). It will have the file you're e-mailing as an attachment. Once you've filled in the info, then you can send off the e-mail.
For multiple or different file types across multiple apps, I understand that you can use the app Goodreader ($4.99, USD) to bring all the files into it. From there, you can use the same "mail to" function to get the pop-up and create/send your e-mail. I've not used Goodreader that way, but I understand others here at this forum have.
Ultimately, it's the decision Apple made to protect the iOS from malicious code. It's a bit inconvenient to have to think opposite of using a more mainstream computer - but it's what we got.
Hope this helps and explains.
Marilyn