You can, but not without some record keeping and probably some testing of your materials and/or finished products.
The fabric (uncoated, not waterproofed), polyester batting and maybe the noses are probably exempt from lead testing, but you'll need to keep track of what items you use. The buttons, however, are not exempt and will need either the CPSIA-format testing results from the manufacturer or you'll need to get them tested yourself.
You may also need small-parts/choking hazard compliance.
You will need CPSIA-compliant labels and probably FTC labels as well.
Best of luck! This section of the Forums has many threads addressing specific issues.
This thread has many good links for research:
http://www.etsy.com/forums_thread.php?thread_id=6385178