I used to move quite frequently. (at least once every 2 years).
From a child's perspective... I very much agree with the principal of the new school. For ALL of us, it was "easier" to have short goodbyes (followed by a trip and moving) and then entry into a new school, than long drawn out goodbyes and immediately into a new school.
Even when we moved mid year, my mum (almost) always made sure we had a bit of vacation (2-5 weeks if not over the summer) to "transition" us into our new environment. I say almost, because there were 2 times early on when we traveled over the summer, came back to our old school for a month or two, and then moved and went directly into a new school.
It sounds to me that you have the "perfect" opportunity. You're travelling for a few weeks... which supplies the transition to starting something new (aka "closure"), and then the summer program is going to introduce her to a small section of her upcoming class in a more 'relaxed' environment.