You need to use Nyquist theorem: for 1MHz signal you should take at least 2MSPS (2 million samples per second)
If you click 16 bit 4 channel DAC on the table another table will open. You will be able to find devices that operate at 2MSPS or more: http://www.ti.com/lsds/ti/data-converters/digital-to-analog-converter-products.page#p84=16;16&p1021=4;4&p596=2;2500