Ok...
Well, there are a number of factors why your calculation ended up with a power that is that low. What you have calculated is the amount of energy stored in the aluminium piece. It is indeed 9mW, but that's not what your laser is outputting.
The aluminium piece is losing heat to the environment both through radiation and convection, and so that needs to be taken into account, and that's where most of the power has gone. Also, not all of the energy from the laser is absorbed by the aluminium piece. No doubt, you coloured it black and that helps with absorption, but it's not going to be perfect, so there'll be some losses. (There'll always be some losses as long as you can see the dot on the black surface. A perfect black surface won't even allow you to see the dot when you shine on it)
The problem is that, if you use a limited time period, then you'll have to perform a rather tricky integral to get the amount of energy lost in total, and then divide it by time to know the power.
Instead, there's an easier method. If you could shine it on to the aluminium piece until the temperature stabilises, then the amount of power in and power out will be equal. From there, at that temperature, I can use the online calculator to calculate the power loss of your aluminium piece, and making a number of small assumptions, we could get a closer figure to the power of your laser.
Do you think your laser can withstand such a long duration of continuous power? You could also try a less powerful laser to attempt that. I only need the temperature to stabilise, and then these figures from you:
1. The surface area of the aluminium piece facing the laser.
2. The surface area of the aluminium piece facing your IR thermometer.
3. The ambient temperature.