Hi Aggie01,
I am not sure how that would work in practice; in the publication, by definition, there will be one name that is printed first, the first author, then the other etc.
In your situation it sounds that you would be the first author, the other student could be the second (presuming any other co-authors, professor etc. are happy regarding this).
I would assure that I would be the first author, the others, as long as they are involved, is a matter of negotiation.
:-)