Babies can't process caffeine in the same way as adults. If anyone is reading this and thinks it's a good idea to give your child black tea of any sort, you should absolutely wait until the kid is at least 10-12 yrs old... The kiddo will be absolutely wired and it negatively impacts their ability to sleep. Overall this is a very bad idea.

Edit: also refined sugar is a big no no for kids younger than 2 yrs old.