The lawyer that represents himself has a fool for his client
Seriously, she's a QC at the Scottish bar,. She could have dealt with the case in Scotland (and the appeal in the Supreme Court) but would have been most unwise to have done so. She couldn't have done the English case because she isn't a member (IIRC) of the English Bar.
Not sure if by 'not at the level' you mean inferior in status or just not as good. There is no prohibition in terms of status - any barrister could (in law and in theory) have dealt with the case, because if you are a barrister at all (whether a QC or not) you have rights of audience in any court, including the Supreme Court. If you mean 'is she as good as the Scottish QCs' I don't know because I've never seen her advocacy. I wasn't however over impressed with the advocacy from either of the Scottish QCs, either the one acting for Joanna Cherry or the one acting for the UK government.