How do I get past this dog?

Have you read its description carefully?

It's a hot dog.

Remember that Xanth is a punny place.

So it's as much a dog that is hot as it is a hot dog that you eat.

I'm sure that no hot dog wants to be eaten.

If you threaten it, you can probably get it to leave you alone.

Few people eat their hot dogs plain.

For one, it helps to have a bun for them.

Other than pieces of bread, can you think of any other types of buns?

Like a hair bun?

Talk to Nada, and eventually, get her to put her hair into a bun.

Now all you need is a condiment to go along with the bun.

There's some in your fridge in Mundane (just ask Nada for a break if you
forgot to bring it with you).