Yes, the $135 tax due on the $1000 sounds like a self-employment tax earned from the 1099 MISC. These are FICA taxes that are normally paid from wages from a W2 but since a W2 wasn't issued for this teaching engagement, a 1099 MISC was issued making her responsible for paying her own FICA taxes.
Self-employment tax is determined by the following formula :$1000 X 9235 X .153 = $142 but there may have been other factors that account for this slight difference. For example, did you include the $7k as part of the income in this return? Did you also indicate that she is a dependent of someone else in the MY INFO section of the return?
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