It meets the min system requirements, but laptops are not really optimized for that kind of heavy computation but that doesn't mean they won't run it.
That being said, I used to run 2010 and 2011 on an Asus Eeepc 1005HA which has significantly less of a spec compared to the 1225B. It ran on there fine as long as you didn't have any large assemblies. It also obviously ran a lttle slow as well, and that is something you should expect.
Also, if you use any of the premium features such as simulation, motion study, photoview, etc. they basically won't function on a laptop. At least in my experience anyways.
Personally I'd keep the desktop and use the laptop just when you have to because you're travelling, etc.
I would also recommend NOT replacing the HDD. It won't give you very much of a performance gain, if any.
Thank you so much. I am keeping the desktop replacement laptop I have. Even though it is very large and heavy it can run anything I throw at it so I will just have to learn to live with the weight.
The Asus G74sx laptop I currently use runs inventory and abaqus FEA software easily so I am sure solidworks will run just as well.
Thanks again for the response.