The fear of jumping in comes from a fear of submersion which in turn comes from fear of getting hair/face wet.
So while continuing to 'play' at jumping in with her when the two of you go swimming, you're unlikely to crack this until you be cracked submersion. Therefore, depending on her tolerance to get her head wet, try:
- washing her face with the pool water
- washing her hair with the pool water
- doing big splashes so water sprays in her face
- you pouring water on her head from watering can. Cheer afterwards, make it a great thing to cheer about doing. Not am anxious look in sight.
- her pouring water on her own head. Cheer afterwards. We did this to the tune of Jack and Jill ("fetch a pail of water" = fill bucket. "Tumbling after" = pour water over head)
- blowing bubbles
- ear in water to "listen for the fishes"
- nose in water
- eyes looking just under surface of the water "to look for fishes".
Then submission games:
- ring a ring a roses "fall down" = under water and cheer.
- hold whilst doing scooping and kicking with arms/legs on front. Forwarn during the length that you are going to go under with her and as you approach the side submerge her for a few seconds to come up at the side. Massive, huge cheers and whoops.
Repeat these every week. Those that accept submersion early are those that just do it and after a few weeks get used to it and realise it's really not that bigger deal.
I think all children react with shock to bring submerged initially. The trick is that you don't react with any negative emotions. Cheer, whoop, be proud, clap, gleeful smiles - these sorts of reaction from you as soon as it happens. Try not to show any concern or anxiety at her reaction, show an 'that's great, going under is no problem' reaction.
Also as a general point, don't shadow her in the pool. More easily done if you take a couple of children. Keep a constant eye on her, but do it from afar. Encourage independence in the pool, whereby you stay sitting on the steps and she plays on her own.