Ollie, sorry about the delay in responding about law careers. I always recommend law to people as I have and continue to enjoy it so much.
#Does law conversion still exist ?" Yes and in fact the course my twins started this month run by BPP is for both people qualifying under the existing system (which my twins will) and also those proposing to take the new SQE1 (and then SQE2) exam. However SQE1 has this week been delayed yet again. The decision on its approval has been delayed until October 2020 - www.lawgazette.co.uk/news/super-regulator-delays-sqe-approval-decision-/5105714.article
Assuming it would not be delayed by the time your daughter graduates she would probably still need to do a course such as BPP's PGDL one to learn the law and then would take SQE1 exams with Kaplan (the new centralised body which will mark the exams). If she obtains a training cnotract offer the firm will pay for this and say the route she should follow. When I checked last year with the regulator in case one of my sons did his gap year and started the conversion course in 2021 they told me he could still do the existing route - GDL, LPC as he would have accepted a place by summer 2021. It is possible the time table to new SQE will slip yet again however which may give even more time to the existing route.
In theory you could study for SQE1 at home and not pay any course fees but that might be quite hard so I think most people will still do a conversion course.
"How do you even start working out which law firms to apply to ?"
There is quite a good list on here which gives pay when training and once qualified which lists the bigger better firms www.rollonfriday.com/inside-info Generally on that list the higher the pay and higher the profit per equity partner the better the firms are regarded. I applied to 139 firms in my last year at university sa I graduated at a time when we had the worst unemployment for 50 years (3m in 1982) and had 25 interviews before getting an offer in my final year as a law undergraduate. I don't think most people then and now have to do so many but it is certainly competitive.
Timing is very important. If you want a law firm to pay for your 2 years of post grad course then you need to apply in time. Most of them recruit trainees from their paid vacation schemes so it is worth applying for those at your daughter's current stage - starting year 2 of university. This would give your daughter the chance to see if she would even want to work in a firm of solicitors. Eg this law firm Allen & Overy has applications open until 18 October for their winter vacation scheme programme - your daughter could apply to that now.
"Winter Vacation Scheme 2020 Students & Graduates
London - Bishops Square
"Job description
Our Winter Vacation Scheme is for students in their penultimate or final year of study or graduates from any degree discipline. Please note that you may only apply for one of our two vacation schemes in any twelve month period.
Applications open on 3 August 2020 and close on 18 October 2020.
The Scheme will take place from 7 to the 11 December 2020, so please ensure you are available to participate, should you be successful in securing a place on the scheme.
We recruit on a rolling basis so we strongly advise you to complete your application as early as possible, as we may close some opportunities ahead of the deadline. " www.aograduate.com/vacation-schemes
They also do summer vacation schemes too which is probably easier to fit around university commitments.
You can however still apply for a training contract without doing a vacation scheme - my older daughter did that and the firm she found paid for her law conversion course and LPC but again you have to apply in time eg summer holiday and start of year 3 (say 2020) at university when they will be recruiting for trainees starting 3 years ahead so year 3 university, GDL and LPC. If you miss the deadline as my daughter did you can take a gap year after the LPC which she did and she worked abroad for a year. If you are applying for vacation schemes in year 2 of university it can be a good idea to have some informal law work experience on your CV or something to show you are interested in law. My daughter did a week in a law firm aged 16 and I think about 2 or 3 days in the BBC legal department a bit later.
I do not think this system will change too much with the SQE exams.
Lots of people are trainees in firms which do not pay for the courses too and more regional firms.