The last flu pandemic (Spanish Flu), lasted from January 1918 until December 1920. If my human calculator is correct that is three years. So 1 to 1.5 years seems almost optimistic.
Top US health official says the coronavirus is 10 times ‘more lethal’ than the seasonal flu would be 500 million assuming Spanish Flu was 50 million and Novel Coronavirus is 10 times worse. On the other hand maybe the Spanish Flu was just like the Coronavirus, we simply do not know. That said the experts "guesstimate" of 12 to 18 months might be too pessimistic like you hope or too optimistic compared to the Spanish Flu.
The good news is if every nation could be like China and attempt to catch every single case the virus will end.
The bad news is more than 10% of infections in Alberta (where I live) are healthcare workers who spread it at home and when they go shopping. In the old days they lived in hospital residence. In efforts to make things better we are unwittingly making them worse.
China on the other hand took seven idled cruise ships and moored them for healthcare workers to live in comfort. It's not just Alberta that has healthcare transmission, 13.6% of Spain's infected are healthcare professionals and 51 doctors have died in Italy.
The moral of the story is if you stop the spread you stop the virus. If you don't stop the spread you accelerate the virus.
Finally consider the current strategy is to slow the spread, not to test for the spread. (I can provide sources if desired). This means it could lengthen the disease duration until herd immunity, unless a miracle wipes it out.
April 3, 2020 Update
Today Ontario said the Pandemic would last 2 years but praised themselves for reducing 5,000 deaths to 1,600 deaths for the month of April.. But of course it was all fiction because it was based on "what ifs".
Personally I hope we can wrap things up with an action plan in 30 days but barring no plan I suspect 3 years and not 2 years like Ontario forecasts or 1 to 1.5 years like OP forecasts.
Sadly it appears no one is in charge.