I didn't see any gazebos but just to be sure I would call City of Orlando and check with them. I don't want to say you could just use a table and then have a Karen calling on you for no reason making the party to be a nightmare for your daughter.
People have birthday parties there all the time. There is a playground but other than a few benches there isn't any like picnic tables. So you can have a picnic style (blankets on the ground) kind of thing. The gazebo is under construction.
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