You will have a great time! I went in December with my 1 year old son on a solo trip. We really enjoyed the public park at the tip of South Beach--tons of families, dogs, and others just enjoying the beautiful views. Very chill vibe and my son was entertained. Also check out the main pedestrian shopping area for casual outdoor seating and people watching (easier to keep baby distracted!) If you are into history at all (or just like beauitful places), check out Vizcaya! It's a lovely place to spend time, and you feel like you are in Europe. The little one will like running around the gardens and water. You will get lovely photos as well. I will say that we spent the $50+ to go to the Jungle Island...and it was not worth it. The conditions for the animals are really restricting. It was a poor zoo, and really expensive. I left feeling sad!
Enjoy your time!!