Yes, it has been prescribed more than once for our one and two year old granddaughters. We meticulously measure out the dosage, and my wife and I double-checked it until we had the routine down. Don't use a spoon; use a graduated dropper. Also, quiz the pharmacist to verify the dosage (avoid metric confusion).
The girls have had no problem tolerating it and it has been effective.
Anyone who can not follow a more-than-usual care procedure in dosing should not be administering it to an infant. I agree with the poster who commented on how potent a sleep inducer Benadryl can be, even for an adult. I myself, 160 lbs. have taken half an adult dose and been knocked out so thoroughly I slept through a cold draft and finally woke up in the morning with the right half of my body barely functional. Be careful.