I think that they are more likely to recommend stenting rather than actual surgery. Hamad Hospital has an excellent cardio-vascular department; fees are heavily subsidised for residents but I am not sure how much they would charge a visitor. The procedure is not cheap, the stents themselves and the disposable equipment required are expensive.

For a private hospital, enquire at Al Ahli Hospital (Bin Omran, opposite to 'Town Centre' souq on the way to TV roundabout). I have no idea of their charges but the ground-floor lobby looks like that of a plush hotel so, if they do the procedure, I am sure that they are not cheap.

Good luck.