I have 7850 graphics card. Can I mine DOGE? Will it be effective? What do you suggest?
your best bet would be an scrypt ASIC.
As a reference:
https://bitmakler.net/asic you can look for SCRYPT asics from this list. They should give you the best performance instead of GPU or CPU.
That being said, theoretically, you should be able to mine with a GPU, according to this list:
https://litecoin.info/Mining_hardware_comparison , your card should hash at a rate between 300 and 400 kH/s. Compare it to the asics in the above list and see the difference
EDIT: do be carefull with the list of bitmakler, next to listing legit asics, i have just noticed he also lists scams/hoaxes... If you ever want to buy an asic, it would be best to find a more trustworthy seller's list