I think how your DD feels about it is most important.
For me personally, I don't think I'd take a baby before about 3-4 months. If it were going to be a hot month, I'd probably wait until they were about 9 months or so. (Of course, it would be winter by then...) Traveling is stressful for anybody, and young babies are delicate. If they run a fever, it frequently involves a spinal tap, which is something you want to avoid if possible.
Will your DD be going with you? Most 2 month olds need their mommies and won't be happy if they're away from home AND away from their primary caregivers.