Hi Brittany!
Yes, you may install and use Little Reader on your husband's laptop in the meantime -- kindly note that you will still need to use your license key, because if you don't you won't be able to access or play your Semester 1 or 2 lessons there.
If you've previously installed LR only on your own laptop before, you shouldn't have problems with doing the same for your husband's laptop since your license key does allow up to 2 software activations. For instructions on how to install LR in your husband's laptop, see:
http://support.brillkids.com/entries/20370881-installing-and-setting-up-your-little-reader-from-your-brillkids-account