No, it won't be dismissed for this reason; what they will most likely do is, when you show up for court and indicate that the notice came too late for your expert request, they will adourn, or reschedule, the case until a later date so you can get your expert. In the meantime, contact the court, explain the situation and see if you can put in the request on  short notice--document your efforts. You probably won't be able to, but you want to show the court you did everything possible.