Yes the stock Q-jet is more than capable to support a 350. As for the computer you will be fine with it. Just need to swap over the sensors from the stock engine to the new one so the computer sees everything it needs to to do its job. Been running my stock CCC system 84 on a vortec headed 355 for years with no issues.
1984 SS, w/87 Grand National 2004R, 355 vortec, CCC, Crane XE262.
1969 Road Runner
2003 GMC Serria