I don't know what's happening in the rest of the world, but fresh food seems to have shot up in price recently. I doubt it's just the hurricane here that's the cause. If inflation does go up, then, according to orthodox economic thought, interest rates should not be far behind.
Both your thoughts are correct, if not particularly sophisticated.
First, your impression is correct -- the price of fresh food, particularly vegetables and fruit, has gone up lately. Not just in Australia, but in most developed countries. This is a result of oil prices. Not only have transportation costs increased but fertilizer costs, too. So even if you're right next door to the freshest green beans ever (mmmm...) you'll find that your neighbor's cost of production has increased. (To be clear, the transport costs are the bigger part of the increase for fresh stuff -- it can't afford to sit around in a warehouse waiting for a spare truck and has to pay rack rate for transportation, maybe even refrigerated transportation.
Second, yes, if inflation increases one would expect to see interest rates increase. In fact, you'd expect to see interest rates increase
in anticipation of higher prices. Indeed, this is exactly what has happened. In Australia, for example, benchmark short interest rates increased by 30 basis points (.3%) in April. The world is worried about inflation.
However. Third, increasing food prices need not portend general inflation. Indeed, on a month to month basis food and energy are traditionally broken out of the inflation figures precisely because they are so volatile. (over longer terms it doesn't make sense to do that -- if prices of those things are up, they're up and people don't stop eating or driving or heating their homes). Prices for many household consumer durables (washers and driers, computers, tvs, etc) are in all but freefall as worldwide competition pressures profit margins. Clothing is also falling in price, at least for comparable goods. I think it makes more sense now to worry about inflation than in, say, early 2001, but the book isn't written on it just yet.