Don't overthink it. We moved when DS was nearly 5. I tried to teach him some before he moved, but he didn't really pick anything up at all (I think he could count to five and say bye and thank you) He's now seven, just started school and doing brilliantly. He switches between languages without an issue and makes friends really easily. I'm not convinced that he listens 100% to the teacher
but I don't know if that's a language issue or just a culture shock from moving from kindergarten where everything is sing-song and they will give a general instruction but then make sure it happens, and he could just follow the others, to a school environment where they give instructions which they are expected to listen, understand, remember, and act on later without reminders. TBH, I suspect the latter.
At two, it might even be easier as most almost two year olds don't speak clearly enough to be understood by strangers anyway. So she won't have the expectation of being able to communicate easily through speech with adults. And it's a fun age, because they pick up random words and insert them into sentences so you get a really hilarious and cute mix. We never really got that stage with DS because he was totally fluent in English when we arrived.
Most adults speak at least a little English, too. I was lucky in that I found an expat type group fairly soon (on meetup.com) and one of them lived near me and was able to tell me that their kindergarten had places, so DS had a little English speaking friend who helped him through the first few months. He came home with new words every day. First colours, then more numbers, then things - tree, car, etc. It tickled me because kids learn the new words as they are pronounced rather than spelled, so when he was saying Auto, he says out-hor, whereas at first I was saying more the English pronounciation like the start of Automatic. And I always thought of "rot" (red) as being pronounced in the English way too but he insisted I was wrong and it was "hhhhrchchOD" 
Please don't worry about not being able to understand her. At first, you will, because you'll learn the words with her. And later, she won't speak German to you anyway. DS doesn't. I have to listen in on him speaking to friends if I want to hear him speak German. It's purely function for them - why would they speak to you in a language you can't understand?
BTW a good tip when you want to search for German things is to open up a google translate tab and type your search term into there, so "Nursery rhymes" becomes Kinderlieder, and then search either youtube or google.de for Kinderlieder. If you use Chrome browser, then you can translate the websites back again if you want to understand what it says. But really, it's fine to just continue with English. In fact, it will be beneficial for her English knowledge to be strong if you're going to live in Germany for a long time, because it's likely that German will overtake as the language she uses the most. If you have another child, this is especially true as they will both know German so they will speak German with each other at home. I know it seems counterproductive, but having a good base in English will likely be just as or even more beneficial than trying too hard to establish German in a situation where she has no useful purpose for it. They are clever and they know
Not to mention that a childish pronunciation of an English accented German will be harder for other people to understand than when she's actually there and starts mimicking native speakers and other children.
For you, (and DH) I really recommend an app called Duolingo. I used that for about a year and a half and by the time I arrived I could make myself understood. It won't get you fluent, but it will get you started, which is important :)
I really like the idea of mum + tot's groups for the first year before kindergarten. And then kindergarten is so lovely and gentle and slow that she really will be absolutely fine even if she hasn't picked up much by then.