The Archive is WAY out of PC power level. And a bit out of stattable power level. She's a Plot Device, and her stats in the book sound about right.
I've been noodling around with a very quick first pass on Ivy, without doing a reread. Most of it I can guess at, a few things I can create effects for, but not cost (blanket refinement bonuses and such).
Ivy
High Concept: Child Archive
Trouble: People want me for what I know
Other Aspects: People don't take kids seriously; Knowledge is Power; I hire the best, and they call him Kincaid; Harry Dresdon gave me a name; tortured by the Denarians.
Skills:
Alertness +2
Athletics +1
Contacts +5
Conviction +3
Deceit +2
Discipline +4
Empathy +1
Intimidation +3
Lore +8
Presence +1
Rapport +1
Resources +5
Scholarship +8
Stunts:
Spot Hipocracy - Ivy may use Scholarship instead of deceit to spot any lie that conflicts with any written document.
Powers:
Evocation [3]
Thaumaturgy [3]
The Sight [1]
Soulgaze [+0]
Wizards Constitution [+0]
Refinement [-60?]
Inhuman recall[-?]: Ivy may take a free action each round to make an assessment with lore or scholarship.
Living library (lore)[-?] - Ivy may double her lore value for all uses, but may gain no benifit from consulting existing libraries.
Living library (scholarship)[-?] - See above.
Specializations
Evocation: All +6
Thaumaturgy: All +6
(The highest single specializations I've seen was Arthur Langtry's +4s, most high council members max out at +3s, 6 is the lowest I can set the total sum of written knowledge on each topic)
Notes: Ivy knows everthing there is to know about magic, but is still a kid and still has some room to grow with having the focus and will power to reach her true potential as a spellcaster. As it is, she can still go toe to toe with the Merlin and hold her one before adding in her ability to assess. She can toss around 22 points of thauatergy with no prep-work, but anything after that takes work to get more power, because she can't add more research.
Ivy is not known to have any magical items. It may be that her skills are so developed that focus items are no longer useful. (added later)The highest refinement + item bonus I recall is again The Merlin at +4/+4. It may be that items make up for lack of refinement up to 8. In which case, make Ivy's refinements 8, and items don't help - her magic is already perfectly refined...