I couldn't think what to call it and still can't. "Conversion" refers to the element in "afire", "abed": converting noun "fire", "bed" to an adjective. In the case of "I'm wooing" vs "I'm a-wooing" there's no such conversion: they're both progressive tenses.

It's hard to get a feel for the difference because we (or most of us) no longer use it. See if this feels right: the "a-" forms an intransitive, naming just the activity of the verb, without a specific object. (In this case it would be conversive of transitivity.)

"Froggy goes a-wooing" vs "Froggy goes wooing the widow next door"

"Papa is a-hunting" vs "Papa is hunting woodsnipe"

But I don't know, and you might well find counterexamples. Just an idea.