She's about the same age as me.

Literal

She [topic-は] roughly me [with-と] same age is.

Bare 年 ('year, age') gives a more precise claim than the related 年頃 ('age range, around the age of') would — '(approximately) the same age' rather than 'the same general age bracket.' Choosing 年 vs 年頃 calibrates how exactly the speaker is comparing two ages. だいたい ('roughly') still hedges the claim, but the granularity of the comparison itself shifts. Plain past だ closes the sentence in casual register; replacing it with です would lift to polite without changing meaning. The と marks 私 as the standard of comparison: 同じ X と Y is 'X is the same as Y.'