Is it bad to apply for a second postdoc immediately after starting a first one?
(This answer assumed the OP was going to be job hunting after a few months for a new position following his current one.  Clarifications given in the comments shows the OP expects to leave the current one-year position after a few months, instead.)

If your first position is only a year long, then it is expected that you will already be searching for a new position before you've even arrived at the current one.  There's simply no choice: most committees are already forming short lists a month or two into the academic year.  This is what makes one year positions brutal: as soon as you get one you've got to start hunting for the next one, but your current post-doc position still expects to see you engaged and active in research and whatever teaching you may have.