There's nothing wrong with giving yourself and your hubby a break from baby, depending on how long the separation is. He's young enough that he's not likely to have much in the way of separation anxiety or acclimation to care-giver (and back) issues.
If you think you'll feel too guilty to enjoy the trip without him, however, how about considering an alternative vacation spot? Consider going to a ClubMed. They have terrific kid clubs and baby clubs. You can spend as much time as you want together doing family things, but can also enjoy some time without kids doing what you want to do, while knowing that your baby is well cared for, and your 7-year old is enjoying tennis, archery, snorkeling,treasure hunts, crafts, tubing, kayaking and flying trapeze with kids her age and wonderful counselors. Sorry, no water slides, but when we were there a year ago (alone -- kids are now 18 and 21), it looked like they have installed an awesome play structure.
Our personal favorite ClubMed is Punta Cana in the Dominican Republic. They have the widest range of activities and serve a very international crowd (lots of French, Dutch, and Germans), so it doesn't tend to have the loud drunken party atmosphere that most of the clubs in the American zone have (like Cancun and Ixtapa). We first started going when our son was 2, and took both kids when he was almost 6 and our daughter had just turned two. Both kids had a blast. After the first day, we hardly saw our son (he preferred to hang out at the mini club and turned into quite the little circus and trapeze artist). After the second day, our daughter would cry until we dropped her off at the petit club, and then didn't want to leave. It is pricey, but they frequently run specials and you can get good prices if you work with midweek arrival and departure.
As far as getting baby to sleep on the plane, I know it sounds wicked, but you can give him a little baby antihistamine, which will make him sleepy.