I think it can't hurt to ask what the cook provides. However, if she's having bottles of milk or is breastfed, then polenta plus carrots, plus snacks and milk would be a fairly decent meal for a 1 year old. - not sure exactly what you are expecting - polenta's a pretty decent protein/carbohydrate source, and it may well have tomato or cheese sauce through it - that would be a cultural thing...
Personally, I don't have much interest in polenta, as it's not one of my own 'cultural' foods, but that doesn't mean it's not nutritious or interesting to a 12 month old (some of the kids at our childcare love it - especially the Italian kids)...