Jan is a great time for spending unlimited time outside, so make the most of that. Dubai (and the UAE in general) has something for everybody, so decide that what you actually like to do rather than just ticking boxes. Your hotel is in 'new' Dubai with very little in the way of history or culture, so you might like to head north towards the creek and check out the more traditional areas.
Are you bringing a baby seat ? Taxis don't carry them. The metro is busy at most times, esp rush hour, and has relatively few seats, but it's cheap, fast, frequent and actually very user friendly.
You could rent a car and take a day trip out into the desert and mountains, or up to Abu Dhabi.
The trip advisor Dubai forum is very friendly
and many of your questions will have been answered before.