alxtrp, your kid reminds me of me. I have memories of being two, which many do not.
They said on PBS in the Human Body show last month that infants with great rhythm talk early, understand language early, and generally excel in that dimension. You child sounds as if rhythm is important to him/her. The music is just a side show to what we are designed to do, talk to each other. I was doing Hello/goodby babbles to Dad before & after lunch when I was 6 months, was doing whole sentences age 1 and told a joke (Mother's story) at 15 months.
I was enjoying 78 rpm records of Tschaikovsky at age 3 on my Bozo the Clown record player. I'm no genius, but I've had an easy time with school and am passionate about music 65 years later. I was too short to climb up on the piano bench until age 8 when a school teacher encouraged me (I was 42 lb age eight), but took to it like I was made for that and made rapid progress.
So while your child is listening, give him lots of language. The brain covets words at that age, teach him 50000 or 200000 words or so. Not as some sort of contest, but in the stories and explanations you give him/her of the world. In two or three languages if you can manage, learning language is something that comes easy to children that age. My parents neither had a foreign language, so I was started on a second language age 8 at school which is a bit late. I'm not too bad at my second language, but it would have been so much easier if my parents had used one.
While you're at it, expose your kid to lots of faces and names. My parents lived in a rural location with few friends and my brain pruned all the facial recognition cells, so I'm terrible at that. See the PBS show about how the child brain prunes the brain cells for the skills it doesn't use.
By all means expose your child to fine motor skills like drawing, carving, or playing an instrument. Also large motor skills like playing ball, which I was never exposed to.
And most important, talk to and read to your child. I didn't learn to read until age 6 at school, but I learned in about 2 weeks I was so prepared by my parent's language lessons. I skipped kindergarden & pre-school, it cost money we didn't have. All this focus on early education, I think is funny. I had my Mother's reading & arts & crafts, my Dad's home repair projects before first grade. I had a two book a week library habit by the 2nd month of first grade, and expanded to 6 books a week by fifth grade. Education not even planned by any pedagog - just taking books off the shelves. Kids are like knowledge sponges, some of them, and they never get full. I never did.
Further advice. Back off when you child is succeeding, maybe age 10. Controlling parents can cause resentment. My parents quit telling me what to do about age 10. I didn't ever go through that hating your parents thing. I enjoyed their stories about old times as a teenager, while we were cooking dinner or digging a ditch or roofing or whatever chores, but there were no orders as long as I was bringing the A's on the report card. I really enjoyed my freedom. I had plenty of moral guidance from the church sermons & Sunday school, I wasn't a lost soul blowing in the wind. That was enough prep to deal with the predators or haters out in the world. With a bike or on foot or on the city bus, and money I earned (I started cleaning gutters for money age 8, a lesson from my Mother, cleaned a boat shop age 10, mowed lawns from age 11) I got around. the parents weren't controlling or hyper-fearful like many modern parents of high performance children.
Have fun with your child, sharing a hobby like music.