  In this paper we extend to the function field setting the heuristics formerly
developed by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral
moments of $L$-functions. We also adapt to the function setting the heuristics
first developed by Conrey, Farmer and Zirnbauer to the study of mean values of
ratios of $L$-functions. Specifically, the focus of this paper is on the family
of quadratic Dirichlet $L$-functions $L(s,\chi_{P})$ where the character $\chi$
is defined by the Legendre symbol for polynomials in $\mathbb{F}_{q}[T]$ with
$\mathbb{F}_{q}$ a finite field of odd cardinality and the averages are taken
over all monic and irreducible polynomials $P$ of a given odd degree. As an
application we also compute the formula for the one-level density for the zeros
of these $L$-functions.
