Portra 400 is your best bet for a faster film, however you'd be much better off shooting a slower finer film and using a large-aperture lens to get the shutter speed up if necessary. I wouldn't do a 12x18 from 35mm unless it was something in the TMX/Acros/Pan-F class, which is a lot finer than any 400-speed film. I'd probably be happy with P400 at 8x10".
I would suggest that you get some Portra 160, Fuji Pro160S or Ektar and maybe a fast(er) lens. In full sun, you can shoot a 160-speed neg film at 1/250 f/11 to get sharp results. If the hard lighting is a problem, use some fill-flash.
Likewise with light-overcast conditions (f/8 light), you can shoot P160 at f/5.6 1/250 or Ektar at 1/200 f/5.6 and get excellent results. The Ektar would easily enlarge to 12x18".
Edit: black dogs and Ektar will be a challenge as it doesn't like underexposure or large dynamic range - think of it as shooting a chrome. If you want a good shot of a black dog, you need to photograph the specular highlights on the fur, which means the dog needs to be against a darker background but have a lot of skylight reflecting off the fur -
darkfield lighting. For example, if you can get the dog in the sun in front of a dark hedge and get as low as possible to maximise the sky/sun specular reflections. And give it a bath+brush first, it will give you an extra stop of gloss to the coat!