I don't think it would be right just to ask her, Julie, as she might not understand the implications; think it would be better to ask her nominated next of kin and if they say yes, then her.
Ancestry and 23 and Me both use saliva tests which might not be the best option in this case. According to the site linked below, Family Tree DNA and My Heritage both use cheek swabs which might be better. But check first before ordering!
https://www.smarterhobby.com/genealogy/best-dna-test/
I would not advise Living DNA since you will be unlikely to get matches from them.