Legal Question in Landlord & Tenant Law in Virginia

Yes, it could be a material breach of the contract, The question is what you may

want to do about it, evict the tenant or send him a notice requesting that he get

rid of the dog or allow the dog to remain with the understanding that any damages done to the unit by or attributable to the dog will be subtracted from the security deposit?

And, no, you may not now seize the tenant's entire security deposit simply because you now have discovered that the tenant has a dog,(My opinion)