Dr. Sue Downing -- who cares for a bunch of dogs owned by celebs including Betty White, Katherine McPhee, Mark Harmon and Benicia del Toro -- has very personal dog problems of her own. Her home was hit by burglars Friday and her seriously-ill dogs are now gone.
It's a weird burglary ... nothing was missing except 2 of her 3 dogs ... a 13-year old pom named Penny and a 3-year old Terrier named Spice. She's not positive if the thieves took the dogs or if the criminals left the gate open and they escaped.
The doctor tells us Penny was taking medication for a heart condition and Spice was born with a birth defect that caused her to limp.
Downing filed a police report ... and the LAPD Pacific Division is on the hunt.