My dd went through the same thing. (She is now 1 yr 1 month)
What we did, was I would get the hoover out, and her daddy would pick her up. For a while he would just take her to another room - she would still cry a bit, but was comforted by daddy. Then he started bringing her to the end of the hall, so she could look down the hall and watch me hoover. Sometimes she took this better than others - if she still cried very much, he would simply take her away again and try it another day.
Then he started bringing her closer ... (you get the picture), and soon, she ended up being okay with it. Then we went through a little phase where she would still get scared if she was on the floor in the same room while I hoovered - I found that if I made a big deal out of putting her 'up high' (on the couch) where she was 'safe', she kind of liked that.
And now, she's totally fine with it - I can leave her sat on the floor and hoover up fairly close to her, and she doesn't bat an eye.
I think the key (for us) was just being very gradual with her, and her daddy talking to her very soothingly and relaxingly. (A gran or friend she is familiar with would probably work just as well, if daddy's not available to help.)