My niece is six, but when she was a toddler, she’d call my mom, her Grandma Kathy, “Namma Taffy”. She’d get picked up and carried by her Namma Taffy, and she’d play with the various articles of clothing my mom would wear. For one thing, she liked buttons, but, as a toddler, she couldn’t quite manage the whole word. So she’d be grabbing each button in turn on her Namma Taffy’s jacket, saying "Butt… butt… butt… "
My boss told me a story about his little boy. It seems the little guy said “shut up” way too often and was tired of being told not to say that, so he decided he was naming his favorite teddy bear “shut up” to get around the rule.
I relayed that story to my 5 year old grandson and he laughed so hard and then asked me to guess what he was going to name his favorite bear. I told him I had no clue so he told me.
“FUCK!” He yelled.
Then we both laughed and laughed.

Not exactly baby speak, but a fun story.
One of my older stories:
I was at a Barnes & Noble browsing the magazines when a toddler came wandering by. She would pick up a book, say “nah but dat don”, set it back in place, take a few steps, pick up another book, say “nah but dat don”, set it back, repeated multiple times.
Before I could figure out what she was saying her mother appeared out of nowhere, saw her daughter holding a magazine and told her “Now put that down”.
I agree with this too. “Mah” is too close to “My” for it to be a coincidence. I instantly thought this the moment I read the OP.
Story told to me years ago by a coworker: He had a beautiful, angelic-looking child, blonde curls, blue eyes, innocent face, the whole package. They were attempting toilet training. It was bedtime. He told her “OK, time to use the potty before bed.” “Don’ wanna use the potty.” “Yes, you have to try.” “No, don’ have to use the potty.” “Yes, just try now.”
“I DON’ HAVE TO USE THE FUCKIN’ POTTY!”
My eldest grandchild used to call her stuffed animals “mungas.”
She also once saw some a dirty diaper about to be discarded and said “bugah,” pronounced bug - ahh. We couldn’t figure out where that came from, but for a while my daughter would use “bugah” as a curse word. Drop something? Oh, bugah. Finally figured out she was trying to say “garbage” and was reversing the syllables. She called me “ma ga” for grandma for a while, too.