Assuming when you scrap the vehicle, you will be buying a replacement, you will normally pay some extra premium to cover the new car until the end of the April renewal (in other words until April 2020) – as happens all the time when people change cars.
There is nothing stopping you having the vehicle MOT’d now to see if your fears re scrapping the car are realised. If it passes, you will then get at least another years motoring out of it (barring some expensive repair bill) – and need not worry about the short term insurance (if you plan to be carless).
Given that time is not of the essence in having the vehicle MOT’d, you can shop around – there are a number of garages near me offering ½ price MOTs – so it might only cost circa £25 for the test.