My pup used to do exactly the same! The reason was that she loves her morning walk, and I thought that she would be desparate for a pee and a poo first thing in the morning so I used to get up when she woke up (and barked to let me know she needed out) and go for a short walk with her, as she usually needs a bit of a walk to do a poo. She got into this routine so that when she woke up, even if she didn't need to go straight away (because she was a bit older and could hold it in) she would still bark to be let out for her walk.
Once I had figured that out, I could go about breaking the cycle by first going down and letting her out at the normal time (about 6.30am) but not going for a walk until at least half an hour after. I would have a cuppa and some breakfast first. This broke the association with going for a walk. After a week or so, when she was still barking to be let out, I would get out of bed, not let her out, but call sternly (out of sight) "That's Enough". She already knew this command from when she was getting a bit out of hand at play time and we would say That's Enough and stop play, amongst other times. You might have a different command - "No" or "Quiet", something like that. It didn't work straight away but within a couple of weeks we were getting a lie in and she knows that barking doesn't get her let out any more. Well, thats the short version anyway - it was more a case of trial and error to find what would work in reality.
We did try ignoring her too but that was taking too long to have any noticeable effect!!