Steve - As I understand fed law, it would be legal for to private party purchase a handgun in VT during the time you are actually a resident of that state.
Where the rub comes in is when you travel back to CT. CT prohibits the transport of a handgun into the state without a permit, with very narrow exceptions. One exception would be the time you are moving your household goods. No going to the range with it, etc.
CT does not require a Permit to possess, but does require one to transport/carry. Coming back to CT over a long weekend with your handgun would be verboten.
My suggestion is to wait until Oct, as I would hate for you to get tangled up with a cop that doesn't understand the nuances of firearm law and you find yourself facing a felony. Any time that you are back, you are more than welcome to shoot my inventory.