You have two options that are comparable in cost. The first would be to take the Alilaguna water bus, Orange Line, to the Giglio stop. Your hotel is a short walk from there, but you would be wise to get specific walking directions as it is easy to get lost in Venice. It is cheaper to buy a round-trip ticket (27 euro), and you can save a few additional euro by purchasing your ticket online before you arrive (25 euro). Children up to age 5 are free.
The other option is to take the ACTV bus from the airport to Piazzale Roma and then the Vaporetto, Line 1, to the Giglio stop. A combo bus/Vaporetto ticket is 14 euro each way so 28 euro roundtrip. Again, your baby will be free.
The other advantage of the Alilaguna service, other than saving a few euro is that there is no bus to boat transfer. You get on the water bus at the airport and get off at the Giglio stop on the Grand Canal. Either option will take at least an hour so be prepared for that. Also, to get to Venice from the airport the Alilaguna water boats have to cross the lagoon to get out to Venice before entering the Grand Canal. Depending on the weather it can be a little rough. If it’s a nice day should be no problem.