Congrats on your pregnancy!
My reply is purely anecdotal but I hope it helps.
I am the mom of a 16 month old girl. My husband makes kombucha. He started because I am a fiend and he wanted to save money, now he's working on making it into a business.
Before pregnancy I drank at least 3 homemade kombuchas. In first trimester I drank about one GTs kombucha every three to I've days, after that I worked my way up to two a day watered down halfway with Apollinaris by the time DD was born.
DD was a perfectly robust 8lb 13 oz. after an initial 10lb loss in 1st tri due to nausea, I gained a healthy 25lb. She has a little jaundice after but that's because I let her sleep too much and didn't wake her up to nurse her enough.
Of course the alcohol content in kombucha is not enough to cause any harm, and DD is developmentally on track or ahead in gross and fine motor skills.
We're still nursing and I am drinking 1-5 (usually 2) homemade kombucha's a day. DD is happy, healthy and growing. She's 31.5" 27lb, strong, a great eater with great digestion.
My advice is to drink it in moderation and to pay attention to what your body wants/doesn't want