If there is a standard cure and quit form for Missouri I have never seen one.
Is this a lease or a monthly rental agreement?
If it is a monthly rental agreement, you could just give them a notice of termination as of the end of February without stating a reason.
For either a lease of a monthly rental agreement, there is a special ten day notice of termination for things like "laying waste" to the property. If the puppy hasn't actually done damage, I am not sure if that would apply. IF it is a standard lease violation, then the period is longer.
I think it would be simpler to just tell them you will need to execute a new pet agreement for the new pet - and include a large pet deposit and a large monthly pet rent. When someone has a pet I don't want, I usually tell them for that pet the pet deposit is $1000 and also there will be additional pet rent of $100. No one ever takes me up on it.
--205.188.xxx.xx