You absolutely don't have to give rice at all, lots of mums find that it really constipates their babies and really it has no nutritional value. The oat cereal will need to be really, really runny at first. I'd work with veggies first then add in fruits, because if she gets a taste for yummy sweet fruit she may decide she doesn't want to try the veggies!
Just to add, if she's pushing the food straight out again with her tongue, it may be that she's not quite ready to wean (tongue thrust being one of the indicators) and you could stop and try again in a couple of weeks.