The cheapest (semi decent) hotel seems to be the holiday inn express close to DXB T3 and the emirates HQ. If I remember correctly its something like 250/- per night with an FZ rate. You'll have to be creative when it comes to cooking/laundry, but it is cheap. Otherwise you can take you chances in Bur Dubai with a hotel apt, but you'll almost certainly get no change out of your 12000/-
FWIW, I took the first month from the company, then spent a week in the cheapest hotel I could find, whilst I was getting my rental agreement sorted, then straight into a good apartment with my family for the next year. Be prepared to sweat a lot, chasing real estate agents around town in every spare moment, but it's worth it. An easier option (especially at this time of year) might be to extend at the hotel for the second month on the company, then go from there.
And as much as people say 'do lots of research on potential areas to live', really nothing compares to actually driving/walking around town. If you're not familiar with the city then you really need to see it for yourself for a few weeks. Plenty of people on here can give you good advice though.
I'm not certain, but you might be fortunate in that there's probably less demand for rentals in the couple of months over the summer, so getting in there sooner rather than later might just work in your favour, before september rolls back around. Just my thoughts...