The supermodel says her Italian greyhound is part of the family

Marisa Miller may not be ready to become a mother just yet, but her dog – an Italian greyhound named Lula – is providing the stunner with some good practice.

“Lula is like family,” she told at the Kentucky Derby on Saturday. “[Raising a dog] is good practice for kids with your husband, because you see who is the disciplinarian and the softy.”

When it comes to her own household, which includes husband Griffin Guess, Miller says Lula is aware that Mom is the one she has to answer to if she misbehaves.

“I am definitely the disciplinarian in our house,” she said. “I take her to school and do the training.”

But despite being the stricter parent, it’s clear Miller is head over heels for her precious pooch.

“Lula is amazing,” she said. “She is the best part of every day. It’s so fun and I am totally a weird dog lady now. I totally let her kiss me, too. Even though I see everything that she eats, her mouth is so cute!”