I wouldn't use dr. to abbreviate the word doctor--and wouldn't suggest that it would be so-used unless in informal codes. In fact, I wouldn't even use Dr. as an abbreviation for doctor unless used before the doctor's surname. I would think most people would find Dr. to be a bit bizarre-looking if used as an abbreviation for doctor without a surname--but most people often surprise me.

After a little research:

In AHD, dr. is listed solely as an abbreviation for debtor, and dr is listed as an abbreviation for dram. Dr. is listed as the abbreviation for both doctor and drive, as has been well-discussed above, but there is not a usage note about whether Dr. would be acceptable standing alone without a surname.