The opera house is less than a thirty minute walk from Daegu Station, but it is probably quicker to take the subway. You are also less likely to get lost. The Daegu Opera House stop is clearly marked in both English and Korean.
It is definitely quicker to take the subway if you are coming in on the KTX. The KTX stops at East Daegu Station (Dong Daegu) which as the name implies is in the eastern part of town.
(Hopefully, an entry on Dong-Daegu Station is coming soon.)