Ultracool dwarfs (UCDs) encompass the lowest-mass stars and brown dwarfs at the stellar--substellar boundary. These intrinsically faint objects are challenging to detect. However, the wide coverage and deep sensitivity of the Euclid survey will increase the number of confirmed and well-characterised UCDs by several orders of magnitude. We carried out a systematic study using Euclid Quick Data Release (Q1) low-resolution near-infrared (NIR) spectra to identify and characterise UCDs. A sample of previously known UCDs in Q1 was compiled to validate the analysis, which was then applied to newly identified UCD candidates in Euclid Deep Field North (EDF-N; 22.9 deg2, down to JE ≈ 24.5 mag). We confirm 33 new UCDs in EDF-N, spanning spectral types (SpTs) M7--T1 (JE = 17--21 mag) and distances of 50--600 pc. Six of them were also independently identified in other Q1 studies. We followed up on two of these objects with ground-based optical and NIR observations using the Gran Telescopio Canarias, providing an independent validation of the Euclid spectral classification and the ability of Q1 spectra to constrain the stellar parameters of UCDs. We determined the SpTs from Euclid Q1 spectra of 33 newly identified UCDs and 167 previously known UCDs by fitting spectral standards from the SpeX Prism Library Analysis Toolkit. The known UCD sample includes 103 objects in common with the Dark Energy Survey (M7--T0, JE = 17--22 mag, and d = 50--600 pc), 6 objects from literature compilations of UCD sources (M8--T7, JE = 18--20 mag, and d = 30--300 pc), and 58 in common with Gaia (M7--L1, JE = 17--24 mag, and d = 70--300 pc). We derived independent stellar parameter estimates through atmospheric model fitting; the resulting effective temperatures are in good agreement with Euclid SpTs. Combined with complementary ground- and space-based data, these results demonstrate the potential for determining proper motions and identifying companions. Additionally, we investigated Gaia UCDs in Q1 by combining their mean XP spectra with Euclid NIR spectra, extending the wavelength coverage and enabling more comprehensive determinations of stellar parameters, including radii. To support broader classification efforts, we analysed the UCDs in colour--colour space and assessed their separation from quasar loci. We present a publicly available, machine-readable catalogue that includes Euclid observations of known and newly identified sources, with spectral classifications and stellar parameters. This work demonstrates Euclid's capability to identify and characterise the faintest stellar populations, establishing a foundation for large-scale UCD studies with forthcoming survey data.