Looks like stoichiometry is always problematic.... ;-)
First, MW is expressed in g/mol (grams/mole) not g/l (grams/liter... that's a density measure, although the standard would be g/ml or better g/cm3).
Second, it's quick to calculate the nanomoles (or micromoles) you are injecting with the data you provide, but to know the molar concentration you should specify a volume for the injection.
Anyway, here is a little break-down with dimensional analysis in parenthesis, which always helps...:
If you wish to know the concentration of the drug you are injecting, we have to make some experimental simulation: you could typically inject (intraperitoneal) 100 microl /10 g of mouse weight, so if you have a mouse of 30 g you can inject 300 microl, so:
34.13 (micromol/kg) * 0.03 (kg) = 1.02 micromol in 300 microl, which means:
1.02 micromol/300 microl /3 = 340 nmol/100 microl, or 3.4 nmol/microl, which is a concentration of 3.4 mM (=mmol/l).