Levemir is suppose to have a flat profile that lasts 24hrs..........the reality is it doesn't last 24hrs, that's why some T1s split the dose in two roughly 12hrs apart. It also has a slight bump in its profile, from memory it's at its peak 3hrs after injecting so has more affect in lowering BG, and then tails off very gradually.
Normally if a T1 forgets to take their nightly basal dose the general consensus is take some* of it when your remember.
If you want to change the time you take it, you will have to do a smaller amount the night before (half?!) and then full amount 12hrs later, if you get what I mean.
* 'some' is worked out as usual dose minus the percentage of time past since when you should have taken it as an example if you take 20u only per day at 9pm usually and forget to take it and remember at 9am, you would give yourself 10u
As with any changes to insulin dosages and timings, being prepared and testing lots is advisable.
EDIT: My knowledge of MODY is not that great so caveat that in to my response!