Kim Kardashian and Kanye West
06/20/2013 at 11:20 AM EDT
is taking his daddy duties very seriously.
rapper – who rushed to Kim Kardashian
's side when she went into labor
– has been doting on his baby daughter.
"Kanye hasn't left Kim and the baby's side," a source close to Kardashian, 32, tells PEOPLE. "He's been in the room for days making sure everything is perfect for the two of them."
With her boyfriend there, the usually open Kardashian – who was admitted to the hospital
with medical complications on June 14 – is savoring her privacy.
According to a source
, "Kim is being very protective of the baby."
With Reporting By JENNIFER GARCIA