Do nursing mothers need an ICVP for yellow fever?

You have a few options. In a rough order from the approaches most recommended by the likes of WHO and CDC and down:

1. Postpone your travel. This is the obvious and safest option given the combination of the vaccine in question being passable to children via breast-feeding and children not being able to receive the vaccine in most circumstances.

2. Get the vaccine anyway. WHO still recommends vaccination when travelling, as does the CDC.

   Pregnant women and nursing mothers should be counselled on the potential benefits and risks of vaccination so that they may make an informed decision about vaccination. Lactating women should be advised that the benefits of breastfeeding far outweigh alternatives. Vaccination is recommended, if indicated, for pregnant or breastfeeding women travelling to endemic areas when such travel cannot be avoided or postponed.

3. Don't breastfeed and get the vaccine. Safer as there is no longer a risk of transmission to the child, but this is not recommended by most health organizations (see the quote from WHO above) as they generally suggest to breast feed for as long as possible.

4. Return via a country that does not require an ICVP. To use a known example, if travelling from Australia to Nigeria and back

   a yellow fever vaccination certificate is required from travellers over 1 year of age entering Australia within 6 days of having stayed over night or longer in a country wiht risk of yellow fever transmission.

   However Qatar has no such requirement. As such, if you were travelling from Australia to Nigeria you could use Qatar Airways, stop over in Qatar for a week and not have to produce a yellow fever vaccination certificate.

5. The CDC provides for a waiver on medical grounds, but it's unlikely that nursing a child will fit this definition.