Are landlords legally allowed to charge pet deposits in Alberta on house/condo/apartment/etc rentals?

Yes, landlords in Alberta may charge a one time non-refundable pet deposit. This fee must be separate from the normal security deposit fee that you are charged if the fee is non-refundable since a regular security deposit is generally refundable in whole or in part.

How much the landlord wishes to charge is at his/discretion but it must not be so high that the fee becomes a penalty. In other words the pet fee should reflect what it might cost the landlord to restore the place after you leave.

In practical terms, as a tenant you will have to decide when you make the rental agreement with the landlord, whether you want to agree to pay any one time fees or not as a condition of renting the property. Pet deposits of $100- $200 are reasonable but could be higher [or lower] depending on the type of pet. A dog or cat is more likely to create a urine problem than a bird. A cat is more likely to cause damage to a carpet or drapes by shredding them. In these case I would expect the deposit to be higher.

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The thing here is that she is not charging you a deposit for the pet, she is charging you for damages done during your tenancy at the rental. Whether she charged you a deposit prior to moving in really had no bearing on any damages done while there. Take the new place. You said you paid a $200 pet deposit. That is fine. If, when you move out, the rugs in the new place are damaged and it costs $400 to repair/replace them then you will owe that landlord $200 additional. The amount you pay prior is not a "cover all" for damages, just a deposit on what damages might occur. It would be the same thing for a security deposit. If you paid $625 as a security deposit but when you moved out the landlord found that you damaged the walls of the rental and it cost $700 to repair then you would owe the landlord an additional $75.