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Not many ships would cater for infants (under 2years). You would need to bring your own baby food & milk on board. You should find that providing there are 2 people in the cabin the infant would only pay Air, airtaxes & port taxes & would not be charged for the cruis.
Traveling with an infant or toddler requires lots of planning and taking along plenty of infant care items. Food and baby bottles top the list for most parents. If you're not nursing, I suggest you bring powdered formula, bottle holders and bottle liners with you on your cruise. You can purchase bottled water aboard ship to mix with powdered formula as needed. Powdered formula takes up far less space than canned formula and doesn't need to be refrigerated.
The only cruise line that sells a wide range of infant care items and baby formula in its shops is Disney Cruise Line. However, the supplies are in limited quantities, so don't go on the cruise assuming you can get all your baby supplies on the ship or in various ports along the way. Disney Wonder's and Disney Magic's Treasure Ketch shops offer a wide range of baby feeding and care items, including regular and soy formula, bottles and bottle liners, and other infant care necessities such as diapers, swim diapers, baby wipes, pacifiers, baby shampoo, and over-the-counter children's and infants' medications.
Holland America Line is one of a few lines that will get baby food at parents' request and have it aboard ship upon check-in. HAL's Ship Services department has a very detailed request form that parents need to complete 30 days prior to their cruise to order baby food. The cost is $1 per jar, and parents can specify the age/stage of food, type of formula and food preferences in respect to jarred fruits, vegetables and meats. I would have opted for this service had I sailed on Holland America when my son was an infant a few years ago. Instead, we lugged a box of jarred food with us on a different cruise line. Since the jars were made solely of glass then (now there are plastic options), we did not check the box on the plane for fear of breakage but rather carried it on.
Princess Cruises says most of its ships stock some baby food, but "it's important to request in advance of the sailing to ensure supply." Likewise, Crystal offers baby food on an advance request basis only. While Cunard Line has baby food in stock, the line suggests a Special Dietary Request be made ahead of time to ensure the variety you need for your child.
For older infants or toddlers who can eat some adult food but may need some harder foods pureed, you can usually request pureed items off the dinner menu in the main dining rooms of most family-friendly cruise lines. You should ask the maitre d' on the first night if he can accommodate this request. A few lines, such as Crystal Cruises, prefer to have advance notice of this request.