Not sure about which places are pet friendly but I do know that dogs are not allowed on the street cars regardless of size. Only service dogs.
The best place for window shopping would be Royal Street. Cars are not allowed on this street and they have many nice shops.
The real "Cajun Country" is not in New Orleans but you can find find tours that will do a driving tour to the real Cajun parishes (can be a 2 hour drive). You may be thinking of the tour company named Cajun Encounters. They offer several types of tours but none of them are "Cajun Tours". Cajun traditions and "cajun country" is very different from New Orleans.

Are your dogs happy in crates when you are not with them? In my experience, very little of NO would be friendly to little dogs, In addition to worries about their being prohibited, I would be concerned about traffic,debris in the streets -- which are not the cleanest in the world -- and critters, human and otherwise.

Are your poodles small enough to go into a shoulder bag? That might allow you to run into places to get a coffee without leaving them tied up outside (something I'm not comfortable doing with my two little dogs.)

We took our two 10 pound chi mixes with us to New Orleans in the winter a few years ago. We had a pet-friendly condo in the CBD. They (and we) enjoyed walks along Magazine St. From the CBD you have to go under the highway, and that area was a little sketchy seeming. I was with my big, bald, scary-looking husband so I felt fine but might not want to walk it as a woman alone. Maybe a short taxi ride to the start of where the shops are on Magazine in the Lower Garden District then get out and walk (assuming a taxi would take the dogs). Great architecture, shops, and restaurants all along Magazine- funkier in the Lower Garden District and more upscale as you get farther Uptown. Of course, there were two of us, one to hold the dogs outside while the other went in for drinks and things, so that made it easier.

We loved the funky shops on Magazine St and ate outside at a great po-boy place called Mahoney's (it wasn't too cold when we were there). I think we did have to go in to order, though. I don't remember if there was an outdoor waiter but they bring your food out when it's ready. We also found a funky dive bar called Half Moon that let us bring them in with us while we had a beer. It looked quite divey but the people were really friendly and recommended Mahoneys to us for the fried chicken liver po-boy (WOW!).

If you can get a taxi to allow the dogs, it would be worth a ride up St Charles (parallel to Magazine) to see all the fancy homes, with the taxi letting you off at Audubon Park. There is a loop around the park of about 3 miles. It was a stunning walk with live oaks dripping with Spanish moss, a lake in the middle, and gorgeous landscaping everywhere, even in February when we were there.

Everyone in NOLA recommended that we keep the number for United Cabs in our phones to call whenever we needed a cab. Cabs are cheap and plentiful in New Orleans. We had a car but did use cabs when we were dining and imbibing in the evenings (our dogs stayed home in crates then!)

You will need to be vigilant if either of your pups is the type who eats any food-related garbage she finds on the street. I have one who does that and we had to use the "Leave It!" command often and even had to pull a part-eaten chicken leg out of her mouth. Lots of smelly trash on the streets to attract the scavenger type dogs!

Have a great trip. We love traveling with our dogs. It sometimes limits your freedom but is so worth it if you are a dog-lover.