@katieechoe. Your plant is a Guzmania.
Don't be concerned if they take awhile to develop roots, most take two to three years before they even flower again. Be careful not to let the soil get too soggy, those types can get root rot if water logged. Just give it time, don't keep disturbing by checking for roots. It is always best to leave the pups on the mother plant as long as you can, at least until they develop a complete rosette and about a third of the size of the mother plant, they get their energy from the mother plant. The one you show, looks pretty developed and should be fine.
