CNN for checking existance of single label
Convolutional models can be used either for classification or not. You cannot train a classifier on a single label, because the loss function of such models is meant to punish the model every time an image is missclassified. If you have a single label, accuracy will be 100% all the time, by definintion. And such a model would be useless.

I think you have two options:


Get a bunch of images that are not dogs, then train a CNN classifier.
Train an Autoencoder for dimensionality reduction on your "dog data". These models can be used for anomaly detection tasks. Once you have trained such a model, when you feed a non-dog image it should be able to recognize it as an anomaly and flag it.


Both methods could work equally good. The first is the simplest one, but if you like playing and experimenting with DL the second is much more fun.