Can I download my unemployment 1099 form now

I imagine it depends on each state's ability to get them published. Keep checking.
I have never heard of UI 1099s online, period.

This depends on what your state provides. Since you didn't give us that info, its impossible for us to tell. Try logging into your states UI site.

The state UI site is probably under the state Department of Labor.

You will need to log into your online unemployment account ( assume you had one for filing this year) and see if it is available, normally they are not till almost the end of the month. But you can check

There really is no rush - the IRS has pushed back the date when it will begin to accept 2013 tax returns to January 31. Normally they "open the gates" on January 21, but this year it's delayed due to the government shut down that occurred in October.