Apparently your 1 line material argument is not deductive and in reality some argumentation schemes may be additionally employed to further strengthen the rhetoric and cogency of arguments by filling in missing steps in between, for example. In such case your argument can be classified as elliptical or ethymematic argument as referenced here.
Often an argument is invalid or weak because there is a missing premise—the supply of which would make it valid or strong. This is referred to as an elliptical or ethymematic argument.
In your case it could be rationally speculated to be filled in as:
My landowner will increase the rent
(I'm short on money and have to find a new place)
(Most landlords don't welcome tenants with pets)
conclusion: I should not get a dog
Also it seems not your argument may not be strongly cogent, it can also be classified as Defeasible argument:
In modern argumentation theories, arguments are regarded as defeasible passages from premises to a conclusion. Defeasibility means that when additional information (new evidence or contrary arguments) is provided, the premises may be no longer lead to the conclusion (non-monotonic reasoning). This type of reasoning is referred to as defeasible reasoning.
In order to represent and assess defeasible reasoning, it is necessary to combine the logical rules (governing the acceptance of a conclusion based on the acceptance of its premises) with rules of material inference, governing how a premise can support a given conclusion (whether it is reasonable or not to draw a specific conclusion from a specific description of a state of affairs).
So in your example, if some landlords happen to be dog-friendly or even offering discount for dog owners, your conclusion may be wrong. This doesn't necessarily mean your argument above has fallacy since there seems to exist certain such custom or general rules...