Khadijah, welcome aboard! It's great that you are planning your very first cruise with Disney for next year.
Technically, most of summer and fall can be considered hurricane season in the Caribbean. The period between June 1 through November 30 is when hurricanes are more typical in that area. However, the ships track this information and can usually detour away from the storms, but ports might be closed or changed. It's not a bad idea to add trip insurance to your cruise just in case.
Summer is a popular time for families to cruise, so that is why you will tend to find the higher prices during those months. You are planning ahead, and the good news with that is that you will get better prices the farther out you book, and have more options to choose from as far as your stateroom as well. Play around on
Disney Cruise Line's website with different ships, dates and itineraries. I bet you'll find one that is priced just right for your family, and I promise you can't go wrong with any of Disney's four magical ships.
Happy planning Khadijah! Let me know if I can help you out with anything else!