Can liquid type mosquito repellents be injurious to the health of small babies?

YES can be dangerous. The most common ingredient in liquid mosquito repellents is deet, a known neurotoxin which can cause lethargy, headaches, tremors, involuntary movements, seizures & convulsions, as well as skin irritation. This can happen at any age but is a greater risk in children, esp. Babies. I would never risk this in my child. There are safe natural alternatives like burt's bees herbal insect repellent.