Oh, another close by one (I'm assuming you're just looking for a fun adventure, rather than being set on long-haul) would be to take the train all the way down through France, Spain and Morocco - probably as far as Marrakech, then fly back one-way. My brother did that trip when his first was about that age, and they had a great time: it's a perfect age for long train journeys.
Hmm.. June is a bit rainy in a lot of the places that might be good contenders for 'first long-haul trip with the baby'. This site gives good information on seasonal travel.
If you're not set on long-haul, then Croatia would be lovely: easy to travel in and with a good combination of relaxed places suitable for enjoying with your baby alongside some interesting culture. Or maybe the SW coast of Turkey.
Long-haul, it's a fairly good time to go to South Africa, or to do a safari somewhere like Tanzania (which is fab). Depends whether you want to wait until your daughter is a bit older and would get more from it, and also on how you feel about the malaria risk for her.