Travelling with a newborn baby

I am traveling to Spain with my newborn baby next week. She is too small for a pushchair so I will be taking her pram which folds down into two parts the carrycot and the wheels. Will be able to take this through the airport and put it in the hold at the steps of the aircraft?

http://www.ryanair.com/en/terms-and-conditions

There is no checked/hand baggage allowance for infants. However, one fully collapsible pushchair/double pushchair/travel system/baby sling per child may be carried free of charge. Additional infant equipment such as car/booster seats and travel cots may be carried in addition to your personal checked baggage allowance. Infant equipment up to a maximum of 20kilos (car/booster seats and travel cots) booked online is charged at the rate of £10/€10 per item/per one way flight or at the airport or through a Ryanair call centre, the higher rate of £20/€20per item/per one way flight will apply. Any infant equipment weighing over the 20 kilos allowance will be charged for the excess at the applicable excess baggage rate per kilo.