Anything (even natural ingredients) that repels bugs is a chemical and could be toxic to the person using it.
Here's what the American Academy of Pediatrics recommends for all children and especially addresses those under the age of 2:
http://www.healthychildren.org/English/health-issues/cond...
"Insect repellents are generally available without a prescription, but they should be used sparingly on infants and young children. In fact, the most common insecticides include DEET (N, N-diethyl-m-toluamide), which is a chemical not recommended for use in children under two months of age. Do not apply DEET-containing repellents more than once a day on older children.
The concentrations of DEET vary significantly from product to product—ranging from less than 10 percent to over 30 percent—so read the label of any product you purchase. Some products have concentrations much higher than 30 percent, and the higher the concentration of DEET, the longer the duration of action. Its effectiveness peaks at a concentration of 30 percent, however, which is also the maximum concentration currently recommended for children. The safety of DEET does not appear to be related to its level of concentration; therefore, a prudent approach is to select the lowest effective concentration for the amount of time your child spends outdoors. You should avoid products that include DEET plus a sunscreen, because sunscreen needs to be applied frequently while DEET should be applied only once a day. If you apply DEET more frequently, it may be associated with toxicity. Also be sure to wash off the DEET with soap and water at the end of the day.
An alternative to DEET is a product called picaridin (KBR 3023). While it has had wider use in Europe, picaridin has more recently become available in the US. It is a generally pleasant- smelling product without the oil residue associated with DEET, and is available in concentrations of 5 to 10 percent.
The American Academy of Pediatrics recommends that repellents used in children over six months of age have 30 percent DEET or 5 to 10 percent picaridin repellent, applied once before going outdoors. These repellents are effective in preventing bites by mosquitoes, ticks, fleas, chiggers, and biting flies, but have virtually no effect on stinging insects such as bees, hornets, and wasps. Contrary to popular belief, giving antihistamines continuously throughout the insect season does not appear to prevent reactions to bites."