Hmm this is a bit dodgy but technically this could work:
You could just go. Once your DD starts to fail to turn up, they can't immediately release her place and allocate it to someone else. I believe they have to wait 6 weeks before removing a child from roll who hasn't been turning up.
After six weeks, so right after she has been removed from roll, you apply for a place for her. You can probably still use your old address, as it is your main address and your move is only temporary. So chances are you get the place (though there may be children ahead of her on the waiting list - it would be a gamble). In practice, I think most schools will expect your child to take up the place after the next half term break or so, rather than immediately. Which could well stretch you to the end of those three months.
It would leave your child with 6 weeks unexplained absence, which might trigger all sorts of involvement; and might leave a bad taste with the school... And I'm not sure if someone who has been removed from roll due to being unexplained absence for 6 weeks can simply re-apply for a place.
But working from the same principles, maybe you could tweak things in that you plan your 3 months so that the first 2-3 weeks fall into school holidays, then your DD stays with GPs for a week or two and attends school while you get settled over there, then she's absent for a week as unauthorised absence (you may have to pay a fine), then you withdraw her from roll - and after a few days (banking on the fact that most schools will take a while to process things) you re-apply for a place. Once it is (hopefully) allocated to your DD, which could take a little while - say a couple of weeks - especially if it happens to be a faith school whose governors are not very efficient, you take the maximum time allowed to accept the place, which could be 10 days or two weeks, then you agree a starting date approx 3 weeks away/ just after the next half-term/holiday break. Maybe your DD would need to go home a week or two sooner than you do and stay with GPs again.
(I'm no expert on this stuff. I have just observed from our school that it has taken a whole half-term, plus half term holidays and Christmas holidays, from when a family left our school, until a new child arrived. That was about 11 weeks. It took about 6 weeks until an offer was made (despite the family having given written notice of their intent to leave), and then the new child wasn't expected to start in the last three weeks of term, so effectively started 5 weeks after the offer was made.)
(And nb yes this is morally dodgy. I have given it some thought because we were faced with a similar situation but decided against 'playing the system' (also would have been a risk due to unsure DS would be first on waiting list after de-reg). However I do think the 'system' is wrong itself in not allowing things like this.)