My ds2 has a large one by his left eye. It's fading now but when he was a year old it looked like a big purple golf ball pulling his eye half shut.
The NHS used to offer laser therapy to shrink them, which prodeuced good results in most cases and could almost invariably at least halt the initial rapid growth phase and often send it into reverse. However following one small, rather dubious study carried out at Birmingham Children's Hospital, the NHS has stopped offering any intervention at all unless the mark threatens "function". Our ds was subjected to batteries of tests to determine the level of damage it was doing to his eyesight and treatments such as interlesional steroid injections, injections of toxins (eg Warfarin) and various other invasive measures were mooted. These are nastier and more dangerous than laser treatment but much cheaper. Ultimately nothing was done, and the mark is now receding slowly on its own, leaving ds2 with a stigmatism in the affected eye and the promise of plastic surgery to "tidy up" the remaining excess tissue, which will be a much longer and more traumatic process than laser treatment while the mark was in its infancy would have been. However it is the particular position of ds2's mark that causes the need for plastic surgery - the vast majority of strawberry haemangiomas do resolve completely on their own with no need for surgical "tidying up". If your dd's mark is on her nose it will hopefully be more straightforward.
If your dd's mark is not threatening "function", eg hearing/sight/speech etc, then it is most unlikely that you will be offered anything other than monitoring. It is my belief that the NHS stopped offering laser therapy because it is considered an expensive treatment to use on a blemish which is largely cosmetic and which often disappears spontaneously. The doctors who make these decisions clearly attach no importance whatsoever to the emotional distress which can be caused to parents and children by leaving a disfigurement (some are severe enough to merit this strong term, others less so)which could easily be treated early. The Birmingham study looks in my opinion like a rush-job, commissioned hastily in order to produce results which could be cited in support of a decision already made on financial grounds. Laser therapy is still the standard treatment in th USA and elsewhere and many studies support its efficacy.
As far as spontaneous involution goes - the figures usually given are: 50% go by age 5, 70% by age 7 and 90% by age 9. If the mark has not gone by age 10 then the possibility of laser therapy is revisited (which contravenes the Birmingham study's findings which claimed that it didn not work - but the consultants prefer on the whole not to be drawn on this).
I would push for monitoring to be done by a consultant on a monthly basis if I were you. Strawberry marks are generally not problematic, but they can ulcerate/bleed/start growing very quickly, rarely - and it's better to have a close eye kept on it than just to be fobbed off with "Oh, we leave those alone, it will disappear when she's older" by a GP.