The big Oxford English Dictionary has this to say:
racquet, -ette
varr. racket n., raquette.
Following over to racket,
racket, n.2
(ˈrækɪt)
Forms: 6 rackat, -it, Sc. rakkett, rakcat, 6–7 rackette, 8 -ett, 5– racket; 6–9 raquet, 7 -ett, 9 racquet. See also raquette.
[a. F. raquette (16th c.) = Sp., Pg. raqueta, It. racchetta, lacchetta, of uncertain origin (see Littré and Devic): hence also Du. raket (in Kilian racket), G. rakete, -ette.]
- a.1.a A bat used in the games of rackets, tennis, etc., consisting of a network of cord or catgut stretched across a somewhat elliptical frame formed of a bent strip of wood, metal, etc., to the base of which a handle is attached.
1500–20 Dunbar Poems xiv. 66 Sa mony rakkettis, sa mony ketche-pillaris. 1540 [see b]. 1574 Newton Health Mag. 6 Striking and receaving the balle with a raquet. 1624 Capt. Smith Virginia ii. 27 The Beaver‥His taile somewhat like the forme of a Racket. 1690 Locke Hum. Und. xxi. §9 A Tennis-Ball, whether in motion by the stroke of a Racket, or lying still at rest. 1763 C. Johnston Reverie II. 206 He was seated at table with a parcel of shuttle-cocks before him, and mending a racket. 1805 Scott Last Minstr. ii. xxxi, Like tennis-ball by raquet tossed.
And lots more examples. So tell her it's "rakket" if she wants to be accurate!