That's just sometimes the way it goes. Yes, you need a guiltless break. And, if you are going to go away for an extended period of time, you need to address this, daily for the next three weeks. Go to the gym for an hour, leave during the day, while she is awake, leave a few times, even if it is for short jaunts (a couple extra 15 minute jaunts, a few times a day is good, too!). I'm sure she will be in good hands with your parents but you need to work on this before you leave so the transition can go as smoothly as possible. Even, daily, having others hold her or visit with her, in or out of your view for a few minutes helps. Your 5 year old can do this too, especially if he, too, is going to be home with grandma and grandpa while you are gone. My sister has 5 adult kids and has been a wonderful role model for me - her mantra when I had babies was "Pass them early, pass them often!" meaning, "let your babies get used to others from a young age. Don't feel guilty about needing some "me-time". Sometimes a short mental-health break lets you reboot and refocus, giving you a little energy boost to effectively handle all of joys and challenges that your family will throw at you.
You can even do all the right things and your child may still experience separation anxiety - now or at a later age. Just keep addressing it.
Enjoy your trip. I'm jealous! It was our goal this year to go to Italy - hopefully 2010 will be the year we take that trip. Is your trip through a tour? Just curious. Do you have any pointers you can throw at me to keep this trip economically feasible - or great locations that I just shouldn't miss? Just personal message me if you want.
Good luck!