Dear Lisa: Rust can appear on most lawn grasses, bluegrass, perennial rye, tall fescue being the most common. Rusts are most troublesome during droughty periods, when grows slows and when nights are cool and we have dew. This has been a very challenging year due to the weather we have had and something out of our control. Potassium and Phosphorus in adequate amounts either existing in the soil or applied by you to build those levels up will help the grass be more resistant to disease outbreaks. Applying Nitrogen as you have done to get the lawn growing again is a good remedy.
Be sure to have the soil retested to verify your applications are having the desired effect. You can also begin to over-seed with hybrid grasses known to have moderate to good rust resistance. This can be done about the same time you are aerating in late summer/early fall. Over several seasons the resistant grasses will gradually predominate the lawn, lessening the rusts presence.
I would consult your family small animal vet to determine if there is a treatment for your dogs while rust is present in your lawn.
Good luck, Richard