I am looking for a description of the Plancherel Measure of $\textrm{SL}_3(\mathbb{Q}_p)$. Has this been calculated yet? I've search many places for it, but I've only found results on real/complex special linear groups and on $p$adic general linear groups. Any help would be appreciated.

This is not a complete answer but only some hints that could help you. Bushnell, Kutzko and Henniart have shown, for a general reductive group, that the restriction of the Plancherel measure to each block of the Bernstein decomposition may be computed via isomorphisms of Hecke algebras : Bushnell, Colin J.; Henniart, Guy; Kutzko, Philip C. Types and explicit Plancherel formulæ for reductive $p$adic groups. On certain $L$functions, 55–80, Clay Math. Proc., 13, Amer. Math. Soc., Providence, RI, 2011. In the following paper, Bushnell and Kutzko show that for certain blocks of ${\rm SL}(N)$the Hecke algebra is isomorphic to a Iwahori Hecke algebra for some ${\rm SL}(N')$ over another field. Bushnell, Colin J.; Kutzko, Philip C. The admissible dual of ${\rm SL}(N)$. I. Ann. Sci. École Norm. Sup. (4) 26 (1993), no. 2, 261–280. 

