NO! DON'T! It's normal to have those thoughts of harm coming to your newborn child dance across your mind!
According to a Mayo Clinic study of 85 new parents--mothers and fathers both--"researchers found that 89 percent experienced distressing, intrusive thoughts related to their infants: images of the baby suffocating or being contaminated with germs, or worries about the baby having an accident, being harmed or kidnapped." See?
Actually what is not typical is for parents to latch onto those fleeting thoughts and to worry that they will/must inevitably transmute into actions. That's a sign to get some help. It's not clear how many new parents who experience postpartum depression also experience postpartum OCD, but the percentage may be as high as half. It's just much less likely for the OCD-related symptoms to get the attention that the depression symptoms do.
This Washington Post article did mention fathers briefly, but it focuses almost exclusively on the experience of mothers. I would be worried, except that Jonathan Abramowitz, the psychologist and Mayo Clinic OCD/Anxiety Disorder Center director who led the research, has already been calling for attention to be paid to both "new moms and their partners" since at least 2001.
Scary Thoughts [washingtonpost]
2001: Acute Onset of
Obsessive-Compulsive Disorder in Males Following Childbirth [psychiatryonline.org]
Another dads and PPD/PPOCD study from a very promising-looking blog [Post Partum Progress]