Would you not be better getting a camera that you can install a SD card into and that way youu wouldn't need to have your laptop on all the time. You should be able to access the recorded footage on the SD card to view footage from your laptop and by connecting to the camera.
I've not put any links up to any as this isn't something I have used myself sou couldn't recommend as mine are all wired but I know you can get them. On my Annke cameras I can install an SD card should the hard drive die on my NVR.
I would suggest looking into IP Cameras. The problem with having your laptop record is that you need it on 24x7 to have full footage. Look into getting a DVR to record it for you but allows you to access from your laptop and phone.