Possible ... yes; likely ... perhaps. Of course, the large dog will be an issue, and will certainly narrow your options ... but some owners might consider it if you furnish a substantial pet deposit ($1000 would not be out of the question, with only a portion, or none at all, refundable). If the dog is one of the more aggressive breeds (irrespective of how it behaves for you) most landlords wouldn't want to take the chance. If you're a smoker, the possibilities may be further diminished.
You may also be restricted by your desired location ... but that's strictly a crapshoot, since rental units come and go quickly inside the Loop. $2600 is not an unreasonable figure ... we just have to find the right circumstances. I wouldn't begin looking until March, since anything decent being offered right now will be gone by then.
Please get in touch with me, so that we can set up an alert as your target date nears. I look forward to hearing from you.