The following is an excerpt from the Westford Pediatrics website:

Insect Repellant Facts

Insect repellents containing DEET have been tested and approved as safe for children, but take some precautions. Choose a repellent with 10% to 30% concentration of DEET (look for N,N-diethyl-m-toluamide on the label). Use lower concentrations if kids will be outside only for an hour or two. If they’re outside longer, consider using a repellent with a higher concentration of DEET. (The higher concentration means that it will last longer.)

Repellent with DEET is not recommended for babies younger than 2 months old.

DEET can be used on exposed skin, as well as clothing, socks, and shoes, but should not be used on the face, under clothing, or on the hands of young children.

Also:

• Do not use a single product containing both sunscreen and DEET — sunscreen needs to be reapplied frequently, while DEET should not be applied more than once a day.
• Concentrations higher than 30% are not more effective and the chemical (which is absorbed through the skin) can be toxic. Be sure to follow the directions on the label.
• If you apply insect repellent to exposed skin, do so sparingly. Do not apply repellent to kids’ hands to avoid ingesting it if they put their hands in their mouth. It can also cause irritation if they touch their eyes.
• Avoid spraying the repellent anywhere near the mouth, so it can’t be ingested.

The Centers for Disease Control and Prevention (CDC) says that repellents containing the ingredients picaridin or oil of lemon eucalyptus also can protect against mosquitoes.

Picaridin is a compound found in many mosquito repellents used in Europe, Australia, Latin America, and Asia. It is often listen under its chemical name KBR 3023. Years of safe use of picaridin in other parts of the world attest to its safety and effectiveness.

Oil of lemon eucalyptus, also known as P-menthane diol, or PMD, for short, is a plant-based repellent that gives protection time similar to low concentrations of DEET products. It is not recommended for kids under 3 years old.

Whatever repellent you choose, check the list of active ingredients to make sure that one of these effective chemicals is on the list, and follow the directions carefully

For more information on repellents (such as choosing the right repellant, using repellants on children or pregnant women, or detailed toxicology information), contact the National Pesticide Information Center (NPIC) toll free at 800-858-7378 or online at npic.orst.edu/wnv/pesticideinfo.htm#repellents.