Cherry Creek can be a difficult area to find vacancy in. As you might know by now, it's a very desireable area to live in. It's also one of the more pricier neighborhoods in the Denver City line area. IF you're serious about staying AS-close to the Cherry Creek Area, you might try to move a little closer to the Denver university area, just east and/OR look for homes as close to Glendale area as possible (which happens to be the city I live in, which is part of the "Cherry Creek" area, but is just a few minutes from the actual Cherry Creek Shopping mall district). While Glendale is over 95% multi-dwelling units, but the very surrounding areas in Denver County, between Monaco, Along Leetsdale, and around Alameda, or just across Colorado Blvd ( all of which runs along the border near Glendale will have some homes who's price ranges that are rented out SHOULD warrant a $1500 rent.)
However, more and more landlords these days might be picky about a large breed dog, in comparison to choosing other candidate who don't have one. Having a dog like that definitely requires a place with a yard, as that's the most fair thing to do for the animal.
What you might probably want to do is post on craigslist a *wanted* (in the title) ad, and place that in the list of the people who have places for rent, as well as alongside those looking for places to live as well. Some landlords look on craigslist to research the market before they put their listings on, and THAT might just get you first dibs on a place that someone hasn't listed yet, that might be close enough to the Cherry Creek area you're wanting to move in.
Let me know if I can help you personally more on this.