There is an abra service within the Madinat Jumeirah. This is not only available for guests of the hotel but also for visitors. The abra trip costs 75 dirhams for adults and 40 dirhams for children over 4 years old (free for children under 4 years).
You can take the abras from close to the Italian restaurant Toscana, and in busy times you may need to book in advance. The abra tour runs for about 20 minutes and is available from 10am until 11pm in winter and an hour shorter, starting at 11am in summer.