+1 for the Trailstar. Keep in mind that while you don't have to have 2 poles for a TS, it does make it easier to have a door, especially in an area w/o any trees to guy out to.
If you want a 1P shelter and take the dog only occasionally/rarely, I think the Solo TS, Gateway Cape or similar-size tarp would be fine. You might be cramped a few nights of the year, but you could put up with that.
If you take the dog almost every trip and really want a 1P+ shelter, then the minimal extra weight of a larger shelter is worth it. The TS does have a large footprint, but I've set it up in PNW forests w/o too much trouble. The nice thing about the TS is that each point can be set up at slightly different heights if needed. This is how, in fact, the TS gets a "door" by staking one point out high, usually with a trekking pole or around a tree. A pyramid (just guessing, I haven't used one), however, likely needs to be staked at a fairly even rectangle, with each corner at the same height.
Most of the single pole shelters seem to be pyramids or similar, but if you are open to bringing 2 poles (either trekking or tent-style poles), there are some good designs that would meet your needs, like the SMD Haven. Just a thought.