Your daughter's doctor should be telling you what she can and cannot do while she has mono. When my daughter had it, she was not allowed to go to school because mono is contagious. She had a teacher come to our house several times a week to go over her school work so she didn't fall behind. She was not permitted to participate in any physical activities since mono can enlarge the spleen which could rupture. She was diagnosed a week before the high school musical and was not allowed to participate in that. She was supposed to dance, but her doctor said absolutely not.
Any virus, including mono, could potentially cause a platelet drop. It's also possible that her counts will stay the same or even go up. Both ITP and mono affect the spleen in different ways, so I wouldn't automatically assume that counts will drop.
If I were you, I'd call her GP to ask about restrictions.