Hi Vanessa, while many landlords and property management companies offer a "no pets" rule, the best thing you can do is to ask that landlord to make an exception. If your dog is well behaved and you're certain it won't bite anyone or ruin the place then have the landlord meet the dog and offer an additional "refundable" pet deposit. In my experience, most landlords will be more willing to accommodate you if you can show them that you are responsible and that they would be fortunate to have you as their tenant. The dog becomes a small issue at that point.
Hello Vanessa. What you need to check is your local rental code. That will give you answers to what animals are allowed. Typically most cities limit it to 3 small animals. Size limitations are more likely to be a rental stipulation than an actual code restriction when it comes to dogs and cats. You can check code enforcement here (cris.lacity.org/cris/informationcenter/code/index.htm).