That certainly puts a different slant on this. If you're buiding a cover, you can extend the outdoor area to gain the space needed. It does appear that there is not an awning over the kitchen slide as standard. Having a covered area, your need for the awning would be seldom, I'd guess. With this additional info, I would say if you love the trailer, it fits the needs of the dog, go for it.
BTW, one dog is not sufficient.....strongly suggest you make a stop at your local shelter or contact a rescue organization - even breed specific rescue - and get your dog a buddy. Adopt/don't shop. Happy camping!