Dog won't walk on a leash-What do I do?

[whalerider23]

I petsitt a 4 month old Australian Shepard mix. She's a good dog but she is a pain to take on a walk. Overall she handles herself pretty well on the leash, she doesn't pull that much and is good around people and other dogs. The one thing that annoys me the most is that she constantly stops walking because she is distracted by different smells. It wouldn't be a big problem if she just sniffed and kept walking but she likes to dig and eat whatever she smells. For instance, we will be walking along and then she pulls over to a yard and buries her nose in the grass and will either eat the grass or roll around in it. She sometimes will even eat poop or trash. She also likes to grab sticks and will lay down and start chewing it. This happens the whole entire walk (beginning, middle, end). It is soooo embarrassing because all these people see me dragging this poor dog down the street. But I have no choice because I can't risk her health by having her eat all this garbage on the street and I need to make sure she gets her exercise.

What should I do?

Should I entice her to keep walking with treats?
Teach her the heel command?
Or should I get a gentle lead?

What do you think?