In the large majority of motor vehicle incidents the child is an occupant of the vehicle : https://crashstats.nhtsa.dot.gov/Api/Public/ViewPublication/...
10 Leading Causes of Injury Deaths by Age Group HighlightingUnintentional Injury Deaths, United States – 2011
2007 - https://www.cdc.gov/injury/wisqars/pdf/unintentional_2007_bw...
2008 - https://www.cdc.gov/injury/wisqars/pdf/leading_causes_injury...
2009 - https://www.cdc.gov/injury/wisqars/pdf/leading_causes_injury...
2010 - https://www.cdc.gov/injury/wisqars/pdf/10lcid_unintentional_...
2011 - https://www.cdc.gov/injury/wisqars/pdf/leading_causes_of_inj...
All Data - https://www.cdc.gov/injury/wisqars/LeadingCauses.html
Suicide means "the deceased ended their life, and had the intent to do so". The US says that people under the age of 9 cannot make a reasoned decision about killing themselves, and thus cannot have the intent to die.
So there will be some people under 9 who killed themselves. It will be a very small number. But their death will be counted as something other than suicide.
Unintentional Poisoning seems really common for adults?! Misuse of prescription drugs apparently.
5-9: Unintentional Drowning 128
Unintentional Fire/Burn 81
I would not call that "far outweighs".