Yes, but make sure you go on a Carnival cruise. I have been on three with my boys (7, 5, 2) They are the only ones who will take kids starting at 2 years old and will change diapers. You will have to pay for him as the 3rd person in your cabin (but on Carnival that includes "camp" for him all day long and into the night if you want it) which is generally about 1/2 price I think. Call the cruiseline and ask about cribs. You may want to bring a pack n play with you. You will have a fabulous time!
Here is what Carnival has to say about their staff:
Camp Carnival's friendly and experienced youth staff want to enhance your child's vacation experience.
Carnival knows the importance of providing your children with top-notch care and supervision, all of our youth counselors have to meet important educational and professional requirements, as well as pass an extensive background check. Every youth counselor is either college educated in education, child psychology or youth recreation, or has professional experience with children, such as teaching or daycare.
Our youth staff is international and all are professionally trained in CPR and are able to provide basic first aid for cuts and bruises. Additionally, should there be a medical emergency, all counselors are instructed to contact the parents immediately, as well as the shipboard infirmary.
and this is their blurb about Camp Carnival:
Camp Carnival's age-appropriate activities are sure to delight all toddlers ages 2-5. From finger painting to cartoon time, arts and crafts to puppet shows, your little ones are sure to have a blast! We even provide babysitting services in the evenings, so Mom and Dad can get in some "quiet time," too.
Toddlers do not have to be potty-trained in order to be part of Camp Carnival; parents simply need to provide the youth staff with diapers and toiletries for their child.
Children also get their very own menus, featuring all their favorite foods. Hot dogs, chicken nuggets, pizza, macaroni & cheese and spaghetti & meatballs are all available on a Carnival cruise, so even our pint-size guests can feel pampered on their "Fun Ship" family vacation.
We are always looking for ways to make our guests' cruises more enjoyable, and now we've eliminated the need to bring a stroller by providing stroller rentals fleetwide, for a nominal fee.
Children under the age of 2 are not able to participate in all the regular programs we offer to the other age groups. We have designated times where children under 2 can participate in our Fun program. The following times are listed below:
Babysitting - From 10:00 pm - 3:00 am each evening of the cruise.
Port Days - From port arrival until 12:00 pm or if a late arrival then for the afternoon until 5:00 pm
Family Play Times - Sea days from 12:00 pm - 2:00 pm or 1:00 pm - 3:00 pm - check Camp Carnival Capers
Parents and their under 2 child can come into the playroom and utilize the facilities that we have OR parents have the option of leaving their child under the supervision of a Youth Counselor, a babysitting fee applies to the second option.
The babysitting fee is $6.00 per hour and is charged to the guest's Sail & Sign Account. Please check the Camp Carnival Capers for specific days and times.
Other activities for toddlers include:
sing-a-longs
Play dough sculptures
picture bing
story time
talent shows
puppet shows
memory games
face painting
and more...
Our youngest Camp Carnival cruisers (ages 2-5) must be signed in at all times while attending. Our experienced youth staff will give them top-notch care and supervision. All parents with children 5 years old and under will receive a complementary beeper or phone on the first day of the cruise to be used throughout the voyage. This way, parents can be contacted in case a child is seriously unhappy, ill, misbehaving, continuously asking for their parents and, especially, in case of emergencies. Note: Children must be at least two years old to attend Camp Carnival.