Do You Brush When Puppy Losing Teeth?

Like the title says, I'm not quite sure if I should be tooth brushing while my pup is losing her teeth. She's a nearly 5 month Poodle puppy, and the teething breath is really bad. I've bought a water additive and been doing practice runs with a finger brush up until now. Is a full tooth brushing is a good idea? I don't want to cause a negative association by poking her already sore gums, but the breath is getting unbearable.