Hi there, I have an eight-week old baby and an almost three year old girl. We have a wood fire heater in our home that barely produces any smoke. The only smoke that comes out is when the door is opened to put more wood in. Would this be a SIDS risk and/or bad for both kids’ development? I know there are risks but as this heater barely produces smoke would it still be a risk?

Red Nose does not have specific guidelines about combustion heaters, however as with any fuel based heating in the house it is important to ensure the air quality within the home is good. 
The smoke from combustion heaters is different from tobacco smoke on its impact on baby. However, both are dose related - the greater the exposure the greater the risk. 
As with gas heaters, airflow is important, & most Government Environment Departments recommend having a window open slightly to allow for this. 

While I am not aware of any direct relationship between smoke from wood fire  combustion heaters & sudden infant death, smoke can cause irritation to airways, particularly with babies & children & in large exposure (eg house fires) can cause carbon monoxide poisoning. 

What can you do to minimise air pollution from your wood-burning heater?

“Check your wood-burning heater conforms with the Australian Standard (AS/NZS 4013:1999) and that the heater and chimney are installed in line with any council-specific building requirements. 
Ensure fresh air enters the room to prevent carbon monoxide build up”
from NSW Health - Environment/Fact Sheet.   
 https://www.health.nsw.gov.au/environment/factsheets/Pages/wood-smoke.aspx -  
see link for full information

Red Nose has included some information in relation to bush fire smoke, following the recent experiences in Australia over summer.(2019/2020)
When considering a baby’s exposure of any form of smoke, we recognise that the greater the exposure, the greater the risk.
While any exposure from a home wood fire smoke would be much less than that of daily exposure to bush fire smoke, some of the information may be helpful.

“Bushfire smoke contains toxic gases such as carbon monoxide and nitrogen oxides, and particles, all of which can be hazardous. 
Small particles in smoke can effects the lungs’ ability to breath normally, aggravate asthma or other respiratory conditions, and can cause a sore throat, runny nose or coughing.
For healthy adults, these symptoms usually go away once the smoke has subsided.
Pregnant women, young children and infants are more sensitive to the effects of breathing in the smoke.
However, we do know that bushfire smoke is toxic, so Red Nose recommends that pregnant women and young children, especially infants, actively limit exposure to the smoke to protect against the ill-effects of the hazardous air. “
https://rednose.org.au/article/bushfire-smoke-and-the-risk-of-sids-and-stillbirth