I assume from your user name that you are in a climate where at least some daylilies have green foliage year round? It makes a difference to whether rust is likely to survive winter and come back the following year (as a general rule of thumb this is in Zones 8 and warmer, sometimes zone 7).
How many daylilies do you have? If only a few then the approach may be different. A good general article on dealing with daylily rust was in the American Hemerocallis Society's "Daylily Journal" and you can read it as a PDF here:
http://www.daylilies.org/RustR...
Also the AHS's web site has a page on daylily rust here:
http://www.daylilies.org/ahs_d...
I'm sure others who deal with rust personally will offer some dog-safe suggestions, which I assume means you'd rather not use pesticides, including "organic" ones?
