Rice pudding is a big no no I'm afraid. It's the milk that seems to be disagreeing with her at the moment. It was fine last time she had this bug (only 2 weeks ago) but this time round it hasn't been my friend!
I would give her plain boiled rice, porridge made with just water with a little sugar/honey/jam on top. Some grated apple should be fairly gentle. Toast with a mashed banana on top.... Poor little thing
It's the lactose in milk that disagrees with her. When my DS has a tummy bug I put him on 'Lacto Free' (which is just ordinary milk, but with the lactose removed), for about six weeks afterwards as ordinary milk just starts the vomiting again. It's more expensive, but for a short period of time I think it's worth it to get them healthy again.
I think in moderation it's fine. But would agree with mousymousy that whatever she fancies as long as no milk - quite often your body fancies what it needs. We used to always have boiled eggs and soldiers when recovering
When we lived in the States (DS 3, DD 1) our doctors' office used to recommend the "BRAT" diet for recovering from tummy bugs B - Banana R - Rice A - Apple (apple chunks, or apple puree or dilute apple juice) T - Toast Seemed to do the trick fairly well in our case - and similar advice I see to several other posters above.