Once I had the same problem, I used notation similar to yours: $\mathbf{0}$ for zero-vector and $\mathbf{1}$ for "all-ones vector".
It is NOT common, so you have to define it
I would not do it unless you have many formulas with it --- if you use it just few times denote it by some letter...
Postscritp. Often $x*x*\dots*x$ is denoted by $x^{*n}$, so you may use $1^{,n}$ for $1,1,\dots,1$.