Are we allowed to present already published material at conferences? Sorry if this sounds like a really stupid question! lol :)

Check the conference regulations.

Generally conferences are for 'new' and 'upcoming' work. They usually have a long lead in time. So if you've already published something, then presenting it as it is might not be fresh enough. It would be preferable to have updated it/developed it further.

If you end up publishing something between applying to a conference and presenting at it, that is less of a problem though.

Edited to add... you might also have to take into account copyright arrangements with the journal, especially if the conference itself publishes abstracts in a journal.

Thanks HazyJane, will do :)