I got DD (now 12) some Sony ones last year as her main present - cost about £75 then, but now £120! They are £95 if you buy in black and blue rather than just black on Amazon.
Sony MDR-ZX770BN is the model number and the sound quality and noise cancelling ability is excellent. Can't believe they've gone up so much in price though, but might be another Sony set in your budget that doesn't have the noise cancelling.
For less than £20 there's some ECandy Bluetooth wireless ones on Amazon - the DC have had them since the beginning of term with no issues - they have survived being folded up and thrown into school bags and apart from the Cyberman impression they look good.
Tbh I would have a conversation with her about acceptable alternatives before buying anything, especially as it is her main present. I can’t believe the price of Beats (and would never pay that) but if she is label conscious - or there is peer pressure - if she can’t have Beats she might prefer to choose something totally different.