Does 1.2cm of additional frame stack make a large difference to the ride of a bike?
My own personal experience is that small changes can make a big difference, but you should be able to get the bars 1.2 cm higher a lot cheaper than a new frame. 

I've found that the most critical measurement in a frame is the Effective Top Tube. If that is "right" for you then with enough bodging you can get the handlebars in the right place. For a road bike that means a stem in roughly the 
90-120cm range for most people. If you aren't over 6 feet and you find you need a stem outside that range, then I would seriously consider a new frame. 

My advice is to spend some time and money on the current bike to find out where the right place is. You might end up with an ugly heavy bodge based on a stem extender, but then you will know exactly what you need in the next bike. 

If the stem extender works, then you might just need a new fork with an uncut steerer so you can get the stack height you want. Forks with carbon steerers have a stack height limit, but even there most bikes come out of the shop with the steerer cut at the minimum rather than the maximum. ( Because it looks better on the shop room floor that way... )