We are off on vacation soon and my parents have kindly agreed to having Georgie stay during our break. My issue is getting Georgie into her travel cage...with only one entrance (the front door) I can see this being a BIG issue getting her into an unfamiliar environment.
For one she won't allow me to pick her up by grasping around her body which means the only way of moving her around is allowing her to perch on my finger. As soon as I approach the travel cage she flies away.
I've tried for months to practice picking her up by holding her body, but she will never allow this.

Any tips please?

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“In order to see birds it is necessary to become a part of the silence.”

when it's dark and quiet, calmly grab her and gently put her in the new cage.
Quickest, least stressful way for me to relocate my birds.

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my budgies don't allow me to hold them either and only step up with milled. I've only had to move my first budgie into a travel cage once and I did it by placing the travel cage entrance right in front of the entrance of her regular cage and putting millet everywhere in the travel cage and also all along the ladder that I used to connect the entrances of the two cages. Even then it took a few hours to move her (and we had to be around so that once she kept moving towards the travel cage we could gradually remove the millet with her every step so that she wouldn't turn back) so I'm hoping that someone can give you better advice.

Get her used to the travel cage first, I think. Mallorn, my hen, is very, very skittish when it comes to new anything--toys, fruits or veggies, cages-- and the only way to get her to accept it is to show her that it's okay. I would start doing this now: get the travel cage and put it by her regular cage. Put toys and millet in it, and touch it or play with it a lot to show her that it's okay. When you let her out to play, make sure she can see the cage.
It will take a few times, but eventually she will just start going in and out of it like a playgym.
Hopefully she realizes that it's not going to hurt her and then when it's time to go it will be easier to put her in Good luck, hope your vacation is a success!

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Not sure what the structure of your cage is, but my little guy used to only go in his carrying cage if I took the roof off and put him in through the top.