Are premature babies born with kidneys?

Yes : The kidneys develop in the first few weeks of fetal development. If a premature baby was born without kidneys then that would indicate another problem is present besides prematurity.

Different issue: Kidneys are part of normal fetal development, premi or not. By 6 weeks into pregnancy the kidneys can make pee which becomes the main contributor to the fluid surrounding baby during pregnancy. In a rare defect of development they may not form, but that is not limited to or part of prematurity.That last one I saw was delivered at term.(and died shortly after)