I think of lots of sub-$500 cameras that will do the trick... BUT... BEFORE you buy a camera, you need to think about "light".
Your cakes have three dimensional texture... especially the detail in the icing work. If you take a photo of your cake using a flash which is built-in to the camera body then it's going to look bad. I don't care which camera you use or how much you paid for it. Flat lighting will look bad.
You want the cake to have a combination of both highlights and shadows. That'll cause the texture and icing work to take on a nice three-dimensional look that "pops" for you.
The light should be "softly" diffused. That means it appears to originate from a broad area. A pinpoint source of light creates a sharply defined separation between highlight and shadow... it looks harsh. Putting light through a screening material (frosted mylar, acetate, or a sheer fabric) will diffuse the light and create gentle transitions.
Reflections are often thought of as a bad thing, but in food photography, a little reflection -- well controlled of course -- creates an effect which makes food appear moist or juicy. It takes away the "dry" look which would look unappetizing.
Here's a video I came across on YouTube which shows what one food photographer might go through to take a photo of a cake:
Food photography, photographing a cake. - YouTube (the audio is poor but you'll get the idea.)
Notice that he hardly mentions the camera (he does at the end). He spends almost the entire time fussing over the light... the source of the light, the strength of the light, the diffuse nature of the light, the color of the light, etc. etc. It's mostly all about the light.
If you want to control the level of blur in the background, then you'll want a camera with an APS-C or larger size sensor (any DSLR made by Canon or Nikon) and a prime lens that can handle f/2.8 or lower focal ratio. My preference would be for a macro lens BECAUSE you may also want to deal with some close-up detail shots. Lenses have minimum focusing distances. One of my favorites is the Canon EF-S 60mm f/2.8 Macro USM lens. The problem is that the lens alone is about $400 (maybe a tiny bit less.)
Again... fuss over the lighting.
If you study that video, you'll realize that this *can* be done on a budget. Jim Talkington made a series of YouTube photography videos which mostly talk about product photography tips (although he does do other types of photography as well.) See:
https://www.youtube.com/user/prophotolife
See episode 2:
https://www.youtube.com/watch?v=-zARqGgHjNc
And see episode 4:
https://www.youtube.com/watch?v=v_UcoCjAcik
You WILL need to fuss over the light (and I do mean "fuss") but you don't necessarily need to spend a ton of money on high-end lighting gear (you may ultimately want to, but you can certainly see how you can get started with some inexpensive items you can pick up at the hardware store and craft store.