before you check-in to the ferry, there is a luggage drop off place next to toast box on 2nd floor of Harbour Front. The limit is one luggage per passenger for 20kg max. Any extra weight is charged $1/kg.
When you reach batam, you can wait for your luggage after the immigration checkpoint. The porter will bring out your luggage. I usually just give them the receipt and carry the luggage out of the terminal myself. Normally the porter would insist to carry it for you and if that's the case, just tip him about Rp 10,000 / luggage.
When you depart batam, you can also get the porter to carry the luggage for you for the same amount of tip. And after immigration checkpoint, you will your luggage on the right side before you exit the arrival area on your left.
In you case, I would definitely get porter to do carry stuffs for you while you can give full attention to your toddler.