The icy queen doesn’t seem like a bad matchup for Laura in general. She has pretty much nothing against projectiles unless she wants to spend meter and she’s very much free to tick throws. All tick throws into command grab will work against her dandy step no matter the version; if you want to be safer and use regular throws use st. LK because the other buttons will make the throw whiff.
Her regular dandy step also doesn’t allow her to escape frame traps; she has to use meter for that too.
You REALLY have to pay attention to her counters though 'cause beat all of your frame traps with 2f+ gaps (and pretty much everything with the EX version). You have to delay buttons and mix up lows and highs during pressure if you don’t want to eat a hard knockdown.
An interesting tech I found against her EX medium command dash:
st. HP xx L fireball, cr. MP xx (whatever you want)
[with meter] st. HP xx EX fireball, cr. MP xx H bolt
If they did an EX dash after st. HP the cr. MP will hit her before she recovers and push her into the fireball for an easy combo. If you use the EX fireball cr. MP xx H bolt will automatically connect with the airborne opponent.
Also st. HK will hit her out her EX dash in the same situation.