Exmoor is miles away from Dorset- at least an hour's drive, probably a lot more depending on whereabouts you are.
To get from Dorset to the New forest Owl centre in 'twenty' minutes' you'd need to be driving at 100mph. From Monkey World to the New Forest Owl Centre is about 3/4 of an hour + more in traffic- Marwell at least another half an hour further on from there.