Hi Amanda,
The tuner that I use charges by the hour, not the job. He will give you an estimate based on past experience, but it often comes out higher or lower, depending on the work he actually has to do, which is hard to predict. I had two accordions tuned a year ago, one was about $200 (less than expected), the other $560 (more than expected). The latter one had not been tuned for over 12 years, some valves needed replacing, and I had some extra musette added - a fair amount of work, but far from $1200.
The $1200 sounds high to me, if it is just for a tuning. Maybe that quote includes a lot of other repairs. For one example, accordions this age often need a lot of the valves replaced (little flaps of leather on each reed), which can be a lot of work. Bad valves cause an accordion to be less responsive by using too much air, and causing you to pump the bellows too much.
If you are inclined to get it serviced, you might want to talk to some other accordion repair shops to see what they could do for less. You may not need it to be fully restored, just good enough for you to play and enjoy it. If you think it really needs some work to make it playable, someone might be able to do a partial job for a lot less, fixing only the worst problems.
To see how out of tune it is, you could take an electronic tuner (a free cell phone app) and play each note individually, on both the push and pull of the bellows, which uses different reeds. Chances are, many of the reeds are not off by that much.