What is a word? By definition, a word is, "one or more spoken sounds carrying meaning and forming a basic unit of speech." I would like to focus on the phrase "carrying meaning." Before I go much further, let me remind you that these are my thoughts and you may disagree. I will use examples to illustrate different points. If a child says, "mama" (and your heart goes a flutter), but is playing with his truck or block, is the child saying a word? It carries meaning for us, but does the child understand that meaning? It is a word in our language, but I would not count it as a "word" for that child. However, this gives you an opportunity to teach the meaning by saying, "yes, baby? I'm mama." He/she will soon associate 'mama' and you! At that point, it would be considered a word. Now, let's say that Junior says "dudu" every time he sees a truck. Is that a word? As long as you and he know the meaning and he says the same thing each time, then yes, I would count it as a word. However, I would call it a 'jargon' word since it is not a known form to most people.
What about this 'deadline' of a year? Like with all milestones, kids will do things on their own timelines. My cousin walked to the door on his first birthday and got excited when he saw balloons and said, "yay! Ba-woons!" is that typical? No, but it does happen. My son just turned a year old and he isn't saying any words consistently enough for me to count them as a word? Am I worried? Not yet because he has been hitting every other milestone, practices with words and sounds, and has a high level of receptive knowledge. I would be worried if he were not responding to my words appropriately, was not playing with sounds or words, or was not attempting to communicate in any way (pointing, fussing, getting my attention, playing kid 'games' like peekaboo, etc).
If your child is signing, but is not deaf, and is signing at least one word consistently, then I would say that he/she has a word by one year. Make sure to always encourage spoken language as well as sign language.