Does anyone know if just having your discharge certificate from the military in enough?

It does have the date I joined and the date I quit on it.

I know Flames will be able answer this one for you- he was in the Military.

For my K-1 package, I gave them : Military Service dates records, copies of all medals received, and copy of ID card. I put those under the Proof of US citizenship. At the time I submitted the package; I had six months before my retirement. But they did not ask for my DD214.

Fun times! I had no clue what they wanted to show for my military service (nearly 15 yrs, Army--infantry--Navy-NCIop, and Air Force -AESop) I talked to many military Admin people and they had no clue! I even sent away for my whole military paperwork that is kept in Ottawa, interesting stuff in there, and its pretty much free, BUT as i recall (been a few yrs now) not much one could use, may have been a document or two that i could have, but was iffy. If I were you, I would send away for it,its good to have a copy of all your military stuff (will look for the link and post it later)
So what did I do? I got the admin people to download my most up to date UER (unit employment Record) It has your whole career on it. As well I got my CO to write a cover letter stating it was an official military document! One probably doesn't require your CO to say it is, but hey, it is the Air Force, I could just walk in and chat with him,lol
But what you have is more than likely suffice. Maybe get it notarized and have some sort of statement stating it is an official military document, but that may be overkill. Best of luck

I sent a letter to the National Archives in Ottawa and asked for the my military records and got back in duplicates both a statement of service and and discharge certificate within 2 weeks.

A contact there would be
Claire Leblanc
Analyst
ATIP and Personnel Records Division
Services Branch
Library and Archives Canada
395 Wellington Street
Ottawa, Ontario
Canada K1A 0N4
Telephone: (613) 996-5115 Fax: (613) 995-6274
Web: http://www.collectionscanada.ca

there ya go, now I dont have to search for it,lol