I am trying to get data from table A to table B. But it is important that domains in table B would remain. So I tried to use Append, but it doesn't work with tables. Any ideas?
Perhaps use arcpy.SearchCursor to iterate through Table A and use arcpy.InsertCursor to insert the values selected in Table A into Table B, you can even use arcpy.UpdateCursor to update existing fields.
Unfortunately I don't know what your data looks like so I am unable to give you an example of each tool that replicates your scenario., but, I hope these tools give you what you are looking for.
if you are looking to actually create Table B from Table A you can use arcpy.CopyRows_management(dbaseTable, outTable)