It might take 24 hours for the App to be pushed out to customers NowTV branded devices (so be patient).
You could try a system update in the menu settings just to see if the App is idle there waiting to go into the Apps Store section on your box / stick.
Just one word of caution the old white nowtv boxes will not be receiving the Disney + App from what i have heard and currently it's only being rolled out to UK customers where Republic of Ireland customers will have to wait a little longer according to NowTV over on their Twitter feed.
Over on NowTV Twitter they are still telling customers later in the Spring this year (who knows if they will still hit this time frame with the coronavirus crises happening).
If you can't wait go to the Disney + UK website help section to see if you own another supported device to watch Disney+ on.