You have no evidence that your tenant has a dog, and your tenant denies having a dog? Then, even if we assume that a court would treat the presence of a pet as a material breach, you do not have any evidence that you could use in court to convince the judge that the dog actually exists.

In general terms, you cannot enter your tenant's premises without permission unless there is an actual emergency, the utilities have been shut off and you need to check for damage or make repairs as a result of the shut-off, or you have a court order. If you are in a county with less than 75,000 residents, you will need to check local ordinances.