As an infant's respiratory system is still developing, a 0- VOC paint is the right idea, but the question is if the 0 VOC paint is as advertised. Paint that is listed as 0 VOC can contain up to 1% of its content by weight with VOC emitting substances, and is not required to list any proprietary ingredient or mixture.
VOC emissions can lead to the formation of ozone and particulate matter, both considered serious pollutants.
Ozone can cause respiratory problems by increasing the permeability of lung cells and so rendering them more susceptible to toxins.
Particulate Matter (PM) is a mixture of tiny particles of dry solid fragments cores with small droplets of liquid. These are made up of metals, soot, solids and dust. When inhaled they can cause a wide range of health problems causing lung function growth. "Certain populations, including the elderly, people with lung or heart disease, infants, children and asthmatics, are at increased risk of experiencing adverse effects with exposure to PM." (2007 ARB SCM for Architectural Coatings).
As an extra precaution I would suggest that you should assume there are VOC's in even a 0 VOC paint and then sufficiently ventilate the room after painting for two weeks.
Two weeks is the LEED standard for ventilating green construction before move in.
Paints and Coatings: Background
Before the 20th century, paints and stains were made up of natural materials as egg and vegetable dyes in the fresco paints of ancient times and fish oil in the wood preservatives of the early American settlers. With progress came petro-chemical based paints and coatings with added durability and protection, and lead enhancing color and their toxic fumes.
Paints and Coatings: Today
As paints and coatings are now highly regulated by eliminating or limiting the use of petrochemicals and solvents, manufacturers are struggling with delivering the high sheen and durability we expect.
Eco minded manufacturers are coming up with clever substitutes by going back to the pre-petro chemical natural binders. Some are finding that a good source for these natural binders is in protein-based waste product.
An example of a paint derived from a waste product is EcoTrend Collagen Paint, a Korean made no-VOC, odorless paint that uses collagen as the paint's binder. The collagen is derived from the eggshell lining recovered from commercial bakery waste and separated with centrifugal force. As a result the paint is very thick and can be applied directly over your existing paint.
Other 0 (low) VOC paints are:
Farrow & Ball Paint, an English made product, that is water based paint with natural pigments and ingredients such as china clay, lime putty and linseed oil. Linseed oil is made from dried, ripened seeds of the flax plant, and can be used as a nutrient.
Green Planet Paints are 0-VOC and made from plant resins and mineral pigments.
Milk Paint is based on a historic paint formula of casein (milk protein) as a binder and is 0 VOC and biodegradable. A drawback is that it should be applied to a semi-gloss white finish and so your existing wall would most likely require painting.
American Clay is another method for finishing your walls. These are 0 VOC, and 100% natural.
For more information:
Read "I am remodeling my home and recently found out that I am pregnant. Is it safe for me to paint if I use no-VOC paints?" a Q&A answered by Florian Speier.