How long is it supposed to it take for HIV to show up in a baby?

None. If i understand it correctly, the question is when a baby can be diagnosed with HIV infection. So, it is assumed that the baby acquires it from his mother. The test that detects viral particles should be used, as antibodies against HIV virus are passively transferred from the infected mother and will vanish only after 6 months of age. The virus can be detected in the blood at any time after birth.
6-8 months. Untreated infants who are infected with HIV through vertical transmission becomes symptomatic by 6-8 months, presenting with chronic diarrhea, mucocutaneous candidiasis, and failure to thrive.