One thing you need for baking foam latex is an oven that can be set at 100 degrees Celsius (which works out to 212 Fahrenheit according to the converter widget on my Mac). Someone in the USA who bakes latex can confirm what the temperature for latex is, in F. Many ovens won't go that low, they are mostly used at much higher temperatures. I can't see very clearly in the photo, but if that top dial is the temperature range in F, the lowest setting I see is 250. It might be possible to set the dial between 0 and 250, even though there is no mark, and get a steady temperature, but I can't be sure.
The other thing to look for is size. If you had a 12" tall puppet, the plaster mould for it would be about 14" long. With arms out to the side a bit, it would be fairly wide too. So if the internal dimensions aren't given, you should measure the width and depth inside the oven. THink of the likely sizes of your puppets and add an inch all around. If you were just doing head moulds, that wouldn't be a problem at all.
My toaster oven, which looks like it might be a similar size, will take a dish 300mm (12") deep x 350mm ( 13.7") wide. I could probably just squeeze in one of my human puppet moulds in, but not the Triclops (my avatar) mould. It's in the kitchen and I use it for my toast, so I haven't tried to fit a mould for latex in it. It will go down to 60C (140F), but doesn't have the fan to move air around. So being smallish, the heating elements might be very close to the mould and create hot spots. The fan in a convection oven would help with that, so I think a convection oven would be better.
What I actually use to bake foam now is a big old metal pie warmer cabinet, with the original gas flame removed and an electric stove element and a thermostat (bought from a stove parts and repair shop) wired up, and it can be set as low as 30F (86F) which is only like a moderately hot day. So it can help for drying moulds or foam puppets after washing them, as well.
Don't know why they can't just give the dimensions in the ad, instead of us having to play guessing games! This Oster oven, from a different seller, says it fits a 12" pizza - so if it is wider than it is deep, might be similar to mine. It also says it has a temperature range of 150 to 450 degrees. It is also described as a "6-slice" oven, so it should be the same size as the one you linked to. Looks like a different model, with curved sides. Costs more too. http://www.costco.com/Oster®-6-Slice-Convection-Countertop-Oven.product.100176811.html
The oven you show looks way too small IMHO. As Nick says, you need to maintain low temperatures over a long time.
A conventional fan oven is basically a metal box with an element and a fan. I recently pulled one apart and rebuilt the box so I could bend perspex. The most useful item, which you have to buy, is a thermostat, which will tell you what temperature you have reached. The bigger the box, the more likely an even temperature will be obtained in the middle with no hotspots. The fan is essential in getting this.
So my suggestion would be to buy a secondhand oven (of the under-counter type) and play around with it. You should be able to set the temperature control reasonably well, but don't trust the numbers on the dial!
Oh, and you won't be able to cook any food in the oven afterwards, be warned!