She has to have her AMHA papers in-hand and in your name before she can be hardshipped into AMHR. [AMHR no longer hardships unregistered minis, they have to already belong to another registery, I think its just AMHA, Fallebella(sp?) and Shetland that they accept.] So, I'd say get her registered in AMHA now, only worry about AMHA right now, as her height isn't important to the registery til she's 3 years old and its time to bring her papers permanent, or if you plan to show AMHA-approved shows (they need ot meet height requirements for age groups for showing); that way she'll have her AMHA papers in order. Then, you can decide later if you want to hardship her AMHR.
Oh, and you can't announce a new addition without pics, forums rules.