If you don't book an excursion you will have to take a taxi to the beach as there is no beach off of the ship. Freeport is not unsafe, it is just you are docked in an industrial area and you have to go somewhere to do something and it is not as built us as some of the other islands. They got hit really hard a few years ago with the hurricanes and alot of places never rebuilt.
If you go to Lucaya beach you can also go to the Sheraton (I think it is the Sheraton, alot of the hotels have changed names). I think they charge like $10 (there should be a towel hut) or so and you can have access not only to the beach but to the pool and the waterslide also...this could be a good option with your young daughter. Unless there is a storm you won't get alot of waves there...Freeport is alot like the DR, there is a barrier reef that keep the big waves out.