Help! 9 month old daughter has high platelet levels

I recently took my otherwise healthy 9 month old daughter to the doctor because of an unusual purply rash on her arm - I forget the name they gave it now - nappy brain - but it was purple dots underneath the skin surface.
They did blood work which came back as follows, with normal range in brackets:

Iron studies:
Ferritin - 18 ng/mL (15-80)
**Iron - 5 umol/L (9-27)
TIBC - 51 umol/L (40-80)
** % Saturation - 10 % (20-55)

Complete blood count:
HB: 113 g/l (92-132)
HCT: 0.32 (0.27-0.4)
RCC: 4.06 x10^12/1 (3.1-4.5)
MCHC: 350 g/l (310-360)
MCV: 79.5 fl (66-84)
MCH: 27.8 pg (22-28)
RDW: 11.4 % (10.3-12.9)
**Platelets: 729 x10^9/1 (170-400)
Total WCC: 10.1 x(10^9)/1 (6.7-17.1)

% ABS
Neuts: 18.0 1.8 (1.3-5.3)
Lymphs:72.0 7.3 (4.1-12)
Monos: 3.0 0.3 (0.1-2)
Eosinos: 7.0 0.7 (0-0.8)

Blood film - Thrombocytosis.

Sorry if those are hard to read. My daughter is otherwise a healthy, alert girl - if a little pale, but we're not dark ourselves - breastfed and on solids. I'm not overly concerned about her iron levels, nor did the doctor seem to be, as they are only slightly low and I know we need to get her to consume more iron rich food, and especially Vit C to help the absorbtion. They have not recommended supplementation.
The platelet levels I found alarming though as everything I've read suggests causes such as infection and chronic iron deficiency - neither of which she appears to have - or scarier causes such as tumours.
The second report took longer and I have not yet heard from her doctor. I'm probably a little neurotic as I've had a previous unexplained stillbirth.
What do you think could be causing this? Should I be worried?
Thanks!