Is there an area to dock my boat here while barbecuing at park or will I have to take her out when not in use?

Unfortunately I don't use the docks, not a boat owner. I do only see the boat launch area. The lake is surrounded by home owners personal dock's. So she would have to come out while you enjoy your BBQ.🙂

I did not see rules posted adviding you, you couldn't but there is 2 docks to your left after dropping her into the water and a separate one to the right so I think you might be in the clear

One public launch, nowhere to dock boat. Docks are private property.