12months- time for cows milk?

Amelia will be one in just a few weeks so 4 days ago i decided to try giving her a bottle of cows  milk , she took it absolutly fine and no alergies or anything ( she had been having it on wheetbix for a wee while ) so for the last 4 days iv been giving her one bottle of cows milk a day ,plus around 2-3 bottles of formular ( if at preschool ) or breastfeeds (if at home) plus at least one breastfeed in the night ( she likes to wake mummy up 1-3 times a night ) , last night at about 11pm she woke up screaming ( a scream like she was in pian ) and her wee tummy was rock hard , i had noticed earlier in the evening her pushing ( like she was going for a poo) but she didnt have any dirty nappies , then this morning she cried for a good 10 minutes and was pushing and had a bowel movemtent but it was VERY hard . so it looks like shes very constipated and i assume it is the cows milk , what is the best way to slowley introduce cows milk into her diet ? i think i may have jumped the gun a bit and started her on too much too soon . i feel really bad because she was in so much pain , poor wee thing

Edited by julz

I agree with Bizzy - it could be a combination of both, but I'd probably leave off on the cows milk anyway, until she is a bit older. Apparently rice milk is a gentler substitute for cows milk and the taste is more like breastmilk, although I couldn't verify that for you LOL