Usually, a conference paper is an extended abstract and not a full paper. We present our results at meeting which is quicker, then we write the full paper for peer review journal. So academically, there is nothing wrong with this approach.
It depends on the copyright policy of the conference. In most cases conference organizers tell you to which journal you can submit your presentation. It may be an indexed journal or can be a lesser quality journal without impact factor. Most presentations undergo an evaluation when you submit it to the conference, which may be followed by a peer reviewing process when it is intended to be published. You have to read carefully the conference documents.
Usually, a conference paper is an extended abstract and not a full paper. We present our results at meeting which is quicker, then we write the full paper for peer review journal. So academically, there is nothing wrong with this approach.
In my limited knowledge, I would like to add that some journals do consideration for review for conference paper provided certain conditions such as rewriting, adding new findings, mentioning the earlier source etc. So, it depends upon the journal.
I think it depends on what you have published: the full research or only the abstract? If it is only the abstract, you can publish the whole research in another journal; if it is the whole research, you cannot.
If your work is integrated then some science Journals accept the full-length typescripts and publish after peer-review. Although, a section of the published paper has been presented in oral/poster presentation. The content of the same script could be presented in a conference and published in a peer-reviewed journal with a condition of no redundancy in results.
The conference paper is a viable foundation for the development of an academic paper. However, the paper has to be re-developed, re-shaped and fine tuned in all its major aspects before it can be published in a journal
If you opt to send the paper published in the proceeding of a conference to a different journal first and major issue will be of "plagiarism". You cannot publish same paper into more than one journal. So, in order to proceed for other journal you must make some modifications in your conference paper (notable modification) and then proceed towards other journal.
Tricky question here....If I understand correctly the original question was if you publish a paper in a Conference Proceeding.... can you then publish it in a Peer Review Journal.... My understanding is NO.... that for Peer Review acceptance one needs to sign an agreement that it has NOT been published anywhere else.... but as some suggest above that an abstract or only part of the article was in a Conference Proceeding than usually is it OK... just be careful about reading the requirements...