I don't want to rain on your upcoming holiday parade, but unless you have a firm offer of a free/paid upgrade please bear in mind that the amount of oil and other money throughout the Arabian Peninsula, and the popularity of the UAE as a shopping/reelaxing destination; suites and other levels of superior rooms are usually the first to go the first to fill up.

Also. have you researched the location of the Hilton Jumierah? It is a LONG way for the other attraction in Dubai (about 20 miles from downtown). The hotel offers a shuttle to a couple of locations but the timings are not always convenient, especially considering the eating/sleeping needs of an infant.