Magic Kingdom to Animal Kingdom without a car?

[bighal]

Buses run between all the parks except MK to/from EPCOT where they expect you to take the monorail. If the monorail is down buses will then run.

[Juliemack]

Is she going into MK first? If not it makes no sense to drop her there, it would be easier to take Sherberth Road and drop her at AK. She would then get a bus from AK and be dropped off near the gates into MK.

[sky13]

MK may not be the most practical place to drop off someone at... In a private car (or Uber or taxi) you will not be able to drop off right outside MK (where the Disney buses and Minnie vans can drop off), and the closest official drop off point is at the TTC (will need to bus, boat or monorail over to MK). The closest unofficial drop off point is the Contemporary which lets you walk over to MK - but there is a good chance that the security at the gate will not let private cars in if they are not guests or do not have ADRs at the contemporary. Additionally MK is a little more out of the way than most of the other Disney parks/resorts...

Would dropping off at AK (can drop off at the park itself) and then bus to MK and bus back to AK work?

Like others have said there are buses or other forms of Disney transport running between all the Disney parks including between MK and AK, so it's a fairly easy way to hop between the two parks and back.