As pointed out by a previous post, the Aussie NZ tour that Charles and Diana did with baby William was 6 weeks, I don't think that the royals do tours of that length anymore. A trip to down under - 2 weeks max. I don't think they would take baby Cambridge with them. Their foreign tours are pretty packed schedule wise. I would think that they would leave the baby and Lupo with Mike and Carole. With technology today, they could check in daily with Skype or FaceTime
Plus people would complain about the extra cost to take the baby, all it's stuff, extra policeman and somebody to watch him/her.