I had mono twice -- yes twice, it's possible. The first as a kid and I was out of school in bed sleeping 20 hours a day for a month straight. The second time as an adult and didn't have that luxury but I dragged my butt through the day and slept every minute otherwise and 22 hours on weekends for about 6 weeks.
However, I think once it was diagnosed and I was on meds, I was ok pretty quickly (by that I mean at least a couple of weeks). I'd think that 16 days would be enough for her to be ok.
Ultimately, I'd still go. If possible, I'd ask the doc for a few scripts of meds to take with you, just in case someone else gets it. People have done it for much less. My 5 yr old got strep throat and scarlet fever about a week before we went away. I had no intention of cancelling, but that's me. He's a trooper and the doc said he would not be contagious after 24 hours on meds.