Perhaps consider Gelsemium sempervirens?
It is well suited for this location and is quite lovely.
Only it is toxic.
Do dogs eat vines?
I didn't know this.
A lot of vines are potentially toxic.
Ipomoea and Clematis can be, but are much safer for pets than my first suggestion.
Wisteria can be toxic, Campsis can be.
Nasturtium species are edible, easy to grow in containers and have a vining habit and might be a good choice but are annuals. Vines used for food are pretty safe.
I like Hops vine, but it can cause contact dermatitis in animals and people.
