Find Your Cruise
If you want something informal then I suggest you take a look at Ocean Village. They have 2 ships doing 7 night cruises every week in the med during September It does involve flights though, either to Palma or Crete. Their booking conditions say that children over 6 months are accepted although for some cruises it is 12 months minimum age - you should contact them to confirm which ones they are (possibly caribbean). For child facilities their web site states :
6 months – under 2 years
Babies and toddlers are welcome at Base Camp as long as a parent or guardian stays with them. During peak season cruises you can also enjoy some ‘mum and dad’ time ashore and leave your little ones in the safe hands of the youth staff*.
The advantage of OV is that their are no fixed meal times (buffet food is available 24 hours a day) so if you have trouble getting the little one to settle down you aren't going to miss your meal. Similarly, if you have to rush off at short notice you can pick up a fresh meal when you return. Cabins are also a decent size. You may wish to consider an outside cabin if you think you may be in there for longer than usual as the window removes the feeling of being in a confined space. What ever you choose have a nice holiday.
Royal Caribbean Spendour of the Seas Greek Isles Cruise from Venice, Sept 20th. Book the cheapest inside cabin you can get on a 'cruise only' basis(about £570 per adult), then book EasyJet (or similar) flights return to venice. we have taken our kids on cruises since they were 5 months old and have always enjoyed it.