Try feeding her lunch a little earlier (say 11am?) and then when she gets up give her some afternoon tea. I wouldnt try and go out too much until she gets used to it. In the car at 11:15am she is bound to fall asleep. Try and make sure if you go out that you are home by 10:30ish so she can have an early lunch.

My DD cut out her day sleep at 12 months and its just about sitting back and working out your own child again as you did when you worked out when to put her down for her 2 sleeps.

It will be hard as he body is used to sleeping twice during the day. Go for more chilled out activities until her body gets used to it.

Dont be suprised if she goes back to 2 sleeps when shes sick