Yes Running will give you strength and Endurance.
And as you are already a long distance walker .
Running won't give you any problem .
Getting up to half marathon distance .
I usually advise 5k for starters depending on fitness and ability .
You should be able to run a good 10k .
Don't be looking for , good times .
It's about getting the Distance .
Then upping to 8 to 10 miles and beyond in your training .
Building up your mileage over the weeks months .
If you want to build up your speed drop back down to 10K , But run It faster.
It's building up the Stamina to do the Half marathons and mind over matter with the Distance .
I don't think it will take you long as you are already fit and we'll .
So go for It .
So when you range up alongside you Oh in the Last mile of 13 race .
Just say .
" I told you I would do It"
Best of luck with your running .