I can definitely see the Connemara in her, but from the shape of her head & her nice big butt I might guess that she has Quarter pony in her, or maybe Welsh?
She's adorable nonetheless, good luck with her!
Since she is a line backed dun, I would say QH is predominant.
Connemaras do not have the dun gene- even though they like to call their buckskins duns, they are truly buckskins and the dun gene is not present in the breed. So even though she could have some Connemara in there, her color came from some other "place" .
She's definitely not a Fjord cross even though she is a linebacked dun. The main is not showing any guard hairs and the pony's conformation is too refined. It's actually against registry rules to crossbreed Fjords, although some of the PMU farms in Canada do it. Deliberate crossbreeding gets the papers pulled for the stallion, dam and any offspring. So there are not that many Fjord crosses.
This weekend, my Fjord stallion was eventing at CDCTA (won his BN division, too) and he got several X-breed inquiries while there. Unfortunately, he must stick to his own kind.