To be safe no you shouldn't it is always better to have the properly rated power supply for your load.
With that said there are certain times when you might be able to use this adapter as opposed to the old one only if they are both the same type of current. Before going any further make sure that the load uses AC current or alternating current. 12vac basically stands for 12 volts of alternating current. If the old power supply produced DC current you should not use the 12vac in its place. If you look at the device your tying to power it should say somewhere on the specs Ac or Dc. If it doesn't it may have a symbol instead.
Now if they both use AC power it comes down to what your load does. If there is any type of computer or processor in the device do not use it. The only time you can interchange these adapters is if the load is a light or motor, where a higher voltage will only increase the intensity of the light or speed of the motor. Remember its better to be safe than sorry. If it's an expensive device don't take the risk.
There is no such thing as a 'd.c. transformer'. If this is a typo, and you really mean an 'a.c. transformer', then the number of laminations will act to reduce the eddy-current losses within the core, but should not affect the turns ratio of your transformer if that's what you are trying to achieve.