Sure, I do it all the time when I travel.  On your original PC look to see where the Company file is located and copy the whole FOLDER to a Thumbdrive or portable drive.  Put that Folder in the same place on your Home PC (See note below on relocating the file if needed to make things simpler.) 

Next install QBDT on your Home computer and when the screen comes up to create a new file look for Open Existing File.  Point QBs to the QBs file in the Folder you moved and you'd done.  VERY IMPORTANT NOTE!!!...  If you go this path you MUST be very diligent about moving the Folder between the two computers EVERY TIME you make a change.  The file you move IS your Company file.  You will royally mess yourself up if you make changes to the DIFFERENT files on the two computers!!  

Another option is to use a program like AnyDesk (or any of the Remote Desktop programs) to access your computer from Home or anywhere you have your notebook with you.  This way you are really always just working on your Work Computer.  There are some security risks, but if you use a good Remote Desktop computer and use VERY STRONG Passwords and encryption on everything (which everyone should be doing anyway), then the risk is not really different than someone breaking in and stealing your computer.

Moving the QB Company Folder/File:  If you find the Company Folder is currently located multi levels down and it's a pain to copy it every time, you can move it.  QB's does not care!  I have ALL of my User Data in C:\Data to make it easy to backup.  So you can create a C:\QB Data or C:\Data\QB Data folder, basically anywhere and called anything you want.  First you Open QBs and then go to to File > Close Company and when it closes you'll be on the screen with some boxes and options to open files.  Close QBs.

Make a copy of your QB Folder and then Move the original Folder to this new location (and Rename it if you want).  Open QBs and it will open to the screen to then Open a File.  Choose Open Existing Company and point to where you moved the Folder to and your Company File.  Open that file and QBs will now use that location every time you open QBs.  Do the same on the other PC, you want to keep things simple and the same on both!